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

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

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

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

n = 2

Solution steps

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

Apply log rules

\frac{ln ( \frac{1}{8} )}{ln ( n )} = - 3

Multiply both sides by

ln (n)

\frac{ln ( \frac{1}{8} )}{ln ( n )} ln (n) = - 3 ln (n)

Apply log rules

n = 2

Verify Solutions:

n = 2

True

The solution is

n = 2

ln (x + 2) = 14

lo g_{10} (x) = 2.0957

ln (x + 2) + ln (x + 1) = ln (4 x + 14)

- \frac{1}{10} ln (2 - 10 w) = 0

lo g_{4} (x + 4) = 3