What is the answer to log_{x}(1/6)=-1 ?

The answer to log_{x}(1/6)=-1 is x=6

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log_{x}(1/6)=-1

lo g_{x} (\frac{1}{6}) = - 1

x = 6

Solution steps

lo g_{x} (\frac{1}{6}) = - 1

Apply log rules

\frac{ln ( \frac{1}{6} )}{ln ( x )} = - 1

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{6} )}{ln ( x )} ln (x) = - 1 \cdot ln (x)

Apply log rules

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

lo g_{7} (6 - 2 t) = 2

ln (ln (x)) = 3

lo g_{2} (\frac{3 x + 1}{4 x - 3}) = 3

lo g_{x} (6) = \frac{1}{2}

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