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

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

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log_{x}(1/8)=-3

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

x = 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 = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

lo g_{3} (x + 7) - lo g_{3} (x - 1) = 1

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

lo g_{10} (2 x - 4) = 2

ln (x) = \frac{3}{2}

lo g_{10} (x^{2} + 64) = 1