diff --git a/NEWS.md b/NEWS.md
index 0fe173063bc5d..9931f1ca56136 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -338,6 +338,8 @@ Deprecated or removed
 
   * `expm` has been deprecated in favor of `exp` ([#23233]).
 
+  * `logm` has been deprecated in favor of `log` ([#CATS]).
+
   * Calling `union` with no arguments is deprecated; construct an empty set with an appropriate
     element type using `Set{T}()` instead ([#23144]).
 
diff --git a/base/deprecated.jl b/base/deprecated.jl
index 1cd9a22640d3c..a616b456c8d43 100644
--- a/base/deprecated.jl
+++ b/base/deprecated.jl
@@ -220,7 +220,7 @@ for f in (:sin, :sinh, :sind, :asin, :asinh, :asind,
         :tan, :tanh, :tand, :atan, :atanh, :atand,
         :sinpi, :cosc, :ceil, :floor, :trunc, :round,
         :log1p, :expm1, :abs, :abs2,
-        :log, :log2, :log10, :exp2, :exp10, :sinc, :cospi,
+        :log2, :log10, :exp2, :exp10, :sinc, :cospi,
         :cos, :cosh, :cosd, :acos, :acosd,
         :cot, :coth, :cotd, :acot, :acotd,
         :sec, :sech, :secd, :asech,
@@ -247,13 +247,13 @@ for f in (
         # base/special/trig.jl
         :sinpi, :cospi, :sinc, :cosc,
         # base/special/log.jl
-        :log, :log1p,
+        :log1p,
         # base/special/gamma.jl
         :gamma, :lfact,
         # base/math.jl
         :cbrt, :sinh, :cosh, :tanh, :atan, :asinh, :exp2,
         :expm1, :exp10, :sin, :cos, :tan, :asin, :acos, :acosh, :atanh,
-        #=:log,=# :log2, :log10, :lgamma, #=:log1p,=# :sqrt,
+        :log2, :log10, :lgamma, #=:log1p,=# :sqrt,
         # base/floatfuncs.jl
         :abs, :abs2, :angle, :isnan, :isinf, :isfinite,
         # base/complex.jl
@@ -1664,6 +1664,9 @@ end
 @deprecate expm! exp!
 @deprecate expm exp
 
+# deprecate logm in favor of log
+@deprecate logm log
+
 # PR #23092
 @eval LibGit2 begin
     function prompt(msg::AbstractString; default::AbstractString="", password::Bool=false)
diff --git a/base/exports.jl b/base/exports.jl
index b1c77b26fb2b8..f3464d9677559 100644
--- a/base/exports.jl
+++ b/base/exports.jl
@@ -589,7 +589,6 @@ export
     linreg,
     logabsdet,
     logdet,
-    logm,
     lu,
     lufact!,
     lufact,
diff --git a/base/linalg/dense.jl b/base/linalg/dense.jl
index 42228106ee3e5..e4af085b5c27c 100644
--- a/base/linalg/dense.jl
+++ b/base/linalg/dense.jl
@@ -426,7 +426,7 @@ function (^)(A::AbstractMatrix{T}, p::Real) where T
     # Otherwise, use Schur decomposition
     return schurpow(A, p)
 end
-(^)(A::AbstractMatrix, p::Number) = exp(p*logm(A))
+(^)(A::AbstractMatrix, p::Number) = exp(p*log(A))
 
 # Matrix exponential
 
@@ -556,7 +556,7 @@ function rcswap!(i::Integer, j::Integer, X::StridedMatrix{<:Number})
 end
 
 """
-    logm(A{T}::StridedMatrix{T})
+    log(A{T}::StridedMatrix{T})
 
 If `A` has no negative real eigenvalue, compute the principal matrix logarithm of `A`, i.e.
 the unique matrix ``X`` such that ``e^X = A`` and ``-\\pi < Im(\\lambda) < \\pi`` for all
@@ -580,25 +580,25 @@ julia> A = 2.7182818 * eye(2)
  2.71828  0.0
  0.0      2.71828
 
-julia> logm(A)
+julia> log(A)
 2×2 Symmetric{Float64,Array{Float64,2}}:
  1.0  0.0
  0.0  1.0
 ```
 """
-function logm(A::StridedMatrix{T}) where T
+function log(A::StridedMatrix{T}) where T
     # If possible, use diagonalization
     if issymmetric(A) && T <: Real
-        return logm(Symmetric(A))
+        return log(Symmetric(A))
     end
     if ishermitian(A)
-        return logm(Hermitian(A))
+        return log(Hermitian(A))
     end
 
     # Use Schur decomposition
     n = checksquare(A)
     if istriu(A)
-        return full(logm(UpperTriangular(complex(A))))
+        return full(log(UpperTriangular(complex(A))))
     else
         if isreal(A)
             SchurF = schurfact(real(A))
@@ -607,19 +607,14 @@ function logm(A::StridedMatrix{T}) where T
         end
         if !istriu(SchurF.T)
             SchurS = schurfact(complex(SchurF.T))
-            logT = SchurS.Z * logm(UpperTriangular(SchurS.T)) * SchurS.Z'
+            logT = SchurS.Z * log(UpperTriangular(SchurS.T)) * SchurS.Z'
             return SchurF.Z * logT * SchurF.Z'
         else
-            R = logm(UpperTriangular(complex(SchurF.T)))
+            R = log(UpperTriangular(complex(SchurF.T)))
             return SchurF.Z * R * SchurF.Z'
         end
     end
 end
-function logm(a::Number)
-    b = log(complex(a))
-    return imag(b) == 0 ? real(b) : b
-end
-logm(a::Complex) = log(a)
 
 """
     sqrtm(A)
diff --git a/base/linalg/diagonal.jl b/base/linalg/diagonal.jl
index 7161d20450b6c..beac1cf844cbd 100644
--- a/base/linalg/diagonal.jl
+++ b/base/linalg/diagonal.jl
@@ -327,8 +327,7 @@ eye(::Type{Diagonal{T}}, n::Int) where {T} = Diagonal(ones(T,n))
 
 # Matrix functions
 exp(D::Diagonal) = Diagonal(exp.(D.diag))
-logm(D::Diagonal) = Diagonal(log.(D.diag))
-logm(D::Diagonal{<:AbstractMatrix}) = Diagonal(logm.(D.diag))
+log(D::Diagonal) = Diagonal(log.(D.diag))
 sqrtm(D::Diagonal) = Diagonal(sqrt.(D.diag))
 sqrtm(D::Diagonal{<:AbstractMatrix}) = Diagonal(sqrtm.(D.diag))
 
diff --git a/base/linalg/linalg.jl b/base/linalg/linalg.jl
index 6eaea00de1b4d..46025dd8d2999 100644
--- a/base/linalg/linalg.jl
+++ b/base/linalg/linalg.jl
@@ -7,7 +7,7 @@ import Base: A_mul_Bt, At_ldiv_Bt, A_rdiv_Bc, At_ldiv_B, Ac_mul_Bc, A_mul_Bc, Ac
     Ac_ldiv_B, Ac_ldiv_Bc, At_mul_Bt, A_rdiv_Bt, At_mul_B
 import Base: USE_BLAS64, abs, big, broadcast, ceil, conj, convert, copy, copy!,
     adjoint, eltype, exp, eye, findmax, findmin, fill!, floor, full, getindex,
-    hcat, imag, indices, inv, isapprox, isone, IndexStyle, kron, length, map,
+    hcat, imag, indices, inv, isapprox, isone, IndexStyle, kron, length, log, map,
     ndims, oneunit, parent, power_by_squaring, print_matrix, promote_rule, real, round,
     setindex!, show, similar, size, transpose, trunc, typed_hcat
 using Base: hvcat_fill, iszero, IndexLinear, _length, promote_op, promote_typeof,
@@ -101,7 +101,6 @@ export
     linreg,
     logabsdet,
     logdet,
-    logm,
     lu,
     lufact,
     lufact!,
diff --git a/base/linalg/symmetric.jl b/base/linalg/symmetric.jl
index 92fe036dbf94f..99d95ba112ab6 100644
--- a/base/linalg/symmetric.jl
+++ b/base/linalg/symmetric.jl
@@ -607,7 +607,7 @@ function exp(A::Hermitian{T}) where T
     end
 end
 
-for (funm, func) in ([:logm,:log], [:sqrtm,:sqrt])
+for (funm, func) in ([:sqrtm,:sqrt],)
     @eval begin
         function ($funm)(A::Symmetric{T}) where T<:Real
             F = eigfact(A)
@@ -639,3 +639,36 @@ for (funm, func) in ([:logm,:log], [:sqrtm,:sqrt])
         end
     end
 end
+
+for func in (:log, #=:sqrtm=#)
+    @eval begin
+        function ($func)(A::Symmetric{T}) where T<:Real
+            F = eigfact(A)
+            if all(λ -> λ ≥ 0, F.values)
+                retmat = (F.vectors * Diagonal(($func).(F.values))) * F.vectors'
+            else
+                retmat = (F.vectors * Diagonal(($func).(complex.(F.values)))) * F.vectors'
+            end
+            return Symmetric(retmat)
+        end
+
+        function ($func)(A::Hermitian{T}) where T
+            n = checksquare(A)
+            F = eigfact(A)
+            if all(λ -> λ ≥ 0, F.values)
+                retmat = (F.vectors * Diagonal(($func).(F.values))) * F.vectors'
+                if T <: Real
+                    return Hermitian(retmat)
+                else
+                    for i = 1:n
+                        retmat[i,i] = real(retmat[i,i])
+                    end
+                    return Hermitian(retmat)
+                end
+            else
+                retmat = (F.vectors * Diagonal(($func).(complex(F.values)))) * F.vectors'
+                return retmat
+            end
+        end
+    end
+end
diff --git a/base/linalg/triangular.jl b/base/linalg/triangular.jl
index ccac60e9cfb7a..eb2af9ab869d5 100644
--- a/base/linalg/triangular.jl
+++ b/base/linalg/triangular.jl
@@ -1789,7 +1789,7 @@ powm(A::LowerTriangular, p::Real) = powm(A.', p::Real).'
 # Based on the code available at http://eprints.ma.man.ac.uk/1851/02/logm.zip,
 # Copyright (c) 2011, Awad H. Al-Mohy and Nicholas J. Higham
 # Julia version relicensed with permission from original authors
-function logm(A0::UpperTriangular{T}) where T<:Union{Float64,Complex{Float64}}
+function log(A0::UpperTriangular{T}) where T<:Union{Float64,Complex{Float64}}
     maxsqrt = 100
     theta = [1.586970738772063e-005,
          2.313807884242979e-003,
@@ -1961,9 +1961,9 @@ function logm(A0::UpperTriangular{T}) where T<:Union{Float64,Complex{Float64}}
 
     return UpperTriangular(Y)
 end
-logm(A::LowerTriangular) = logm(A.').'
+log(A::LowerTriangular) = log(A.').'
 
-# Auxiliary functions for logm and matrix power
+# Auxiliary functions for matrix logarithm and matrix power
 
 # Compute accurate diagonal of A = A0^s - I
 #   Al-Mohy, "A more accurate Briggs method for the logarithm",
@@ -2117,7 +2117,7 @@ end
 unw(x::Real) = 0
 unw(x::Number) = ceil((imag(x) - pi) / (2 * pi))
 
-# End of auxiliary functions for logm and matrix power
+# End of auxiliary functions for matrix logarithm and matrix power
 
 function sqrtm(A::UpperTriangular)
     realmatrix = false
diff --git a/doc/src/stdlib/linalg.md b/doc/src/stdlib/linalg.md
index 66dd343d3f195..99c8c2f3d3412 100644
--- a/doc/src/stdlib/linalg.md
+++ b/doc/src/stdlib/linalg.md
@@ -92,7 +92,6 @@ Base.repmat
 Base.kron
 Base.SparseArrays.blkdiag
 Base.LinAlg.linreg
-Base.LinAlg.logm
 Base.LinAlg.sqrtm
 Base.LinAlg.lyap
 Base.LinAlg.sylvester
diff --git a/test/linalg/dense.jl b/test/linalg/dense.jl
index 30fcf9ace436c..1635b415dd92b 100644
--- a/test/linalg/dense.jl
+++ b/test/linalg/dense.jl
@@ -453,20 +453,20 @@ end
                                      1/3 1/4 1/5 1/6;
                                      1/4 1/5 1/6 1/7;
                                      1/5 1/6 1/7 1/8])
-        @test exp(logm(A4)) ≈ A4
+        @test exp(log(A4)) ≈ A4
 
         A5  = convert(Matrix{elty}, [1 1 0 1; 0 1 1 0; 0 0 1 1; 1 0 0 1])
-        @test exp(logm(A5)) ≈ A5
+        @test exp(log(A5)) ≈ A5
 
         A6  = convert(Matrix{elty}, [-5 2 0 0 ; 1/2 -7 3 0; 0 1/3 -9 4; 0 0 1/4 -11])
-        @test exp(logm(A6)) ≈ A6
+        @test exp(log(A6)) ≈ A6
 
         A7  = convert(Matrix{elty}, [1 0 0 1e-8; 0 1 0 0; 0 0 1 0; 0 0 0 1])
-        @test exp(logm(A7)) ≈ A7
+        @test exp(log(A7)) ≈ A7
     end
 
     A8 = 100 * [-1+1im 0 0 1e-8; 0 1 0 0; 0 0 1 0; 0 0 0 1]
-    @test exp(logm(A8)) ≈ A8
+    @test exp(log(A8)) ≈ A8
 end
 
 @testset "issue 5116" begin
@@ -487,28 +487,28 @@ end
 
 @testset "Additional matrix logarithm tests" for elty in (Float64, Complex{Float64})
     A11 = convert(Matrix{elty}, [3 2; -5 -3])
-    @test exp(logm(A11)) ≈ A11
+    @test exp(log(A11)) ≈ A11
 
     A12 = convert(Matrix{elty}, [1 -1; 1 -1])
-    @test typeof(logm(A12)) == Array{Complex{Float64}, 2}
+    @test typeof(log(A12)) == Array{Complex{Float64}, 2}
 
     A1  = convert(Matrix{elty}, [4 2 0; 1 4 1; 1 1 4])
-    logmA1 = convert(Matrix{elty}, [1.329661349 0.5302876358 -0.06818951543;
+    logA1 = convert(Matrix{elty}, [1.329661349 0.5302876358 -0.06818951543;
                                     0.2310490602 1.295566591 0.2651438179;
                                     0.2310490602 0.1969543025 1.363756107])
-    @test logm(A1) ≈ logmA1
-    @test exp(logm(A1)) ≈ A1
+    @test log(A1) ≈ logA1
+    @test exp(log(A1)) ≈ A1
 
     A4  = convert(Matrix{elty}, [1/2 1/3 1/4 1/5+eps();
                                  1/3 1/4 1/5 1/6;
                                  1/4 1/5 1/6 1/7;
                                  1/5 1/6 1/7 1/8])
-    logmA4 = convert(Matrix{elty}, [-1.73297159 1.857349738 0.4462766564 0.2414170219;
+    logA4 = convert(Matrix{elty}, [-1.73297159 1.857349738 0.4462766564 0.2414170219;
                                     1.857349738 -5.335033737 2.994142974 0.5865285289;
                                     0.4462766564 2.994142974 -7.351095988 3.318413247;
                                     0.2414170219 0.5865285289 3.318413247 -5.444632124])
-    @test logm(A4) ≈ logmA4
-    @test exp(logm(A4)) ≈ A4
+    @test log(A4) ≈ logA4
+    @test exp(log(A4)) ≈ A4
 end
 
 @testset "issue #7181" begin
@@ -677,7 +677,7 @@ end
     @test exp(a) == exp(a)
     @test isposdef(one(elty))
     @test sqrtm(a) == sqrt(a)
-    @test logm(a) ≈ log(a)
+    @test log(a) ≈ log(a)
     @test lyap(one(elty),a) == -a/2
 end
 
diff --git a/test/linalg/diagonal.jl b/test/linalg/diagonal.jl
index 3ec850f125591..47b7eaf509194 100644
--- a/test/linalg/diagonal.jl
+++ b/test/linalg/diagonal.jl
@@ -63,7 +63,7 @@ srand(1)
             for func in (exp,)
                 @test func(D) ≈ func(DM) atol=n^3*eps(relty)
             end
-            @test logm(Diagonal(abs.(D.diag))) ≈ logm(abs.(DM)) atol=n^3*eps(relty)
+            @test log(Diagonal(abs.(D.diag))) ≈ log(abs.(DM)) atol=n^3*eps(relty)
         end
         if elty <: BlasComplex
             for func in (logdet, sqrtm)
@@ -382,7 +382,7 @@ end
     @test ishermitian(Dsym) == false
 
     @test exp(D) == Diagonal([exp([1 2; 3 4]), exp([1 2; 3 4])])
-    @test logm(D) == Diagonal([logm([1 2; 3 4]), logm([1 2; 3 4])])
+    @test log(D) == Diagonal([log([1 2; 3 4]), log([1 2; 3 4])])
     @test sqrtm(D) == Diagonal([sqrtm([1 2; 3 4]), sqrtm([1 2; 3 4])])
 end
 
diff --git a/test/linalg/symmetric.jl b/test/linalg/symmetric.jl
index 09b4370ed922c..d5d7164f80d63 100644
--- a/test/linalg/symmetric.jl
+++ b/test/linalg/symmetric.jl
@@ -13,17 +13,17 @@ end
     A1 = randn(4,4) + im*randn(4,4)
     A2 = A1 + A1'
     @test exp(A2) ≈ exp(Hermitian(A2))
-    @test logm(A2) ≈ logm(Hermitian(A2))
+    @test log(A2) ≈ log(Hermitian(A2))
     A3 = A1 * A1' # posdef
     @test exp(A3) ≈ exp(Hermitian(A3))
-    @test logm(A3) ≈ logm(Hermitian(A3))
+    @test log(A3) ≈ log(Hermitian(A3))
 
     A1 = randn(4,4)
     A3 = A1 * A1'
     A4 = A1 + A1.'
     @test exp(A4) ≈ exp(Symmetric(A4))
-    @test logm(A3) ≈ logm(Symmetric(A3))
-    @test logm(A3) ≈ logm(Hermitian(A3))
+    @test log(A3) ≈ log(Symmetric(A3))
+    @test log(A3) ≈ log(Hermitian(A3))
 end
 
 @testset "Core functionality" begin
diff --git a/test/linalg/triangular.jl b/test/linalg/triangular.jl
index eb0fc7cd57717..8589b530160ff 100644
--- a/test/linalg/triangular.jl
+++ b/test/linalg/triangular.jl
@@ -174,9 +174,9 @@ for elty1 in (Float32, Float64, BigFloat, Complex64, Complex128, Complex{BigFloa
             @test B == viewA1.'
         end
 
-        #exp/logm
+        #exp/log
         if (elty1 == Float64 || elty1 == Complex128) && (t1 == UpperTriangular || t1 == LowerTriangular)
-            @test exp(full(logm(A1))) ≈ full(A1)
+            @test exp(full(log(A1))) ≈ full(A1)
         end
 
         # scale