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

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

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log_{y}(32)=5

lo g_{y} (32) = 5

y = 2

Solution steps

lo g_{y} (32) = 5

Apply log rules

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

Multiply both sides by

lo g_{32} (y)

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

Simplify

1 = 5 lo g_{32} (y)

Switch sides

5 lo g_{32} (y) = 1

Divide both sides by

5

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

Apply log rules

y = 2

Verify Solutions:

y = 2

True

The solution is

y = 2

8 lo g_{10} (y) = 8

lo g_{10} (x) - lo g_{10} (2 - 3 x) = 1

5 - 4 lo g_{3} (x) = lo g_{x} (3)

0.59 = lo g_{10} (x)

lo g_{x} (8) = 6