What is the answer to log_{x}(1/81)=-2 ?

The answer to log_{x}(1/81)=-2 is x=9

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log_{x}(1/81)=-2

lo g_{x} (\frac{1}{81}) = - 2

x = 9

Solution steps

lo g_{x} (\frac{1}{81}) = - 2

Apply log rules

\frac{ln ( \frac{1}{81} )}{ln ( x )} = - 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{81} )}{ln ( x )} ln (x) = - 2 ln (x)

Apply log rules

x = 9

Verify Solutions:

x = 9

True

The solution is

x = 9

lo g_{2} (x + 3) + lo g_{2} (x - 1) = 5

ln (x) = 7.5

lo g_{10} (x) + lo g_{10} (x + 1) = 5

lo g_{2} (ln (x)) = 1

lo g_{3} (5 x - 8) = 1