What is the answer to log_{x}(1/8)=3 ?

The answer to log_{x}(1/8)=3 is x= 1/2

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log_{x}(1/8)=3

lo g_{x} (\frac{1}{8}) = 3

x = \frac{1}{2}

Solution steps

lo g_{x} (\frac{1}{8}) = 3

Apply log rules

\frac{ln ( \frac{1}{8} )}{ln ( x )} = 3

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{8} )}{ln ( x )} ln (x) = 3 ln (x)

Apply log rules

x = \frac{1}{2}

Verify Solutions:

x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

\frac{ln ( x )}{x} = 0

ln (7 - x) - ln (10) = ln (x)

lo g_{8} (x - 3) + lo g_{8} (x + 4) = 1

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

ln (x) + ln (x + 1) = 1