What is the answer to log_{x-1}(8)=1 ?

The answer to log_{x-1}(8)=1 is x=9

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log_{x-1}(8)=1

lo g_{x - 1} (8) = 1

x = 9

Solution steps

lo g_{x - 1} (8) = 1

Apply log rules

\frac{1}{lo g _{8} ( x - 1 )} = 1

Multiply both sides by

lo g_{8} (x - 1)

\frac{1}{lo g _{8} ( x - 1 )} lo g_{8} (x - 1) = 1 \cdot lo g_{8} (x - 1)

Simplify

1 = lo g_{8} (x - 1)

Apply log rules

8 = x - 1

Solve

8 = x - 1 : x = 9

x = 9

Verify Solutions:

x = 9

True

The solution is

x = 9

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6 ln (5 x + 2) + 6 = - 6

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