What is the answer to log_{x-1}(32)=5 ?

The answer to log_{x-1}(32)=5 is x=3

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log_{x-1}(32)=5

lo g_{x - 1} (32) = 5

x = 3

Solution steps

lo g_{x - 1} (32) = 5

Apply log rules

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

Multiply both sides by

lo g_{32} (x - 1)

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

Simplify

1 = 5 lo g_{32} (x - 1)

Switch sides

5 lo g_{32} (x - 1) = 1

Divide both sides by

5

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

Apply log rules

x - 1 = 2

Solve

x - 1 = 2 : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

lo g_{\frac{1}{2}} (5 + 4 x) = - 2

ln (100000 - x) = 11.4571

8 - 8 lo g_{2} (- 10 x - 6) = 24

lo g_{6} (x^{2} - 6 x + 9) = 2

ln (5 x + 2) = 4