What is the answer to log_{m}(32)=5 ?

The answer to log_{m}(32)=5 is m=2

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log_{m}(32)=5

lo g_{m} (32) = 5

m = 2

Solution steps

lo g_{m} (32) = 5

Apply log rules

\frac{1}{lo g _{32} ( m )} = 5

Multiply both sides by

lo g_{32} (m)

\frac{1}{lo g _{32} ( m )} lo g_{32} (m) = 5 lo g_{32} (m)

Simplify

1 = 5 lo g_{32} (m)

Switch sides

5 lo g_{32} (m) = 1

Divide both sides by

5

lo g_{32} (m) = \frac{1}{5}

Apply log rules

m = 2

Verify Solutions:

m = 2

True

The solution is

m = 2

lo g_{x} (81) = - 4

2 = ln (x)

lo g_{x} (4) = \frac{1}{2}

2 lo g_{2} (x) - lo g_{2} (x + 3) = 2

ln (x^{2}) = 18