What is the answer to log_{x}(1/81)=4 ?

The answer to log_{x}(1/81)=4 is x= 1/3

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log_{x}(1/81)=4

lo g_{x} (\frac{1}{81}) = 4

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

lo g_{x} (\frac{1}{81}) = 4

Apply log rules

\frac{ln ( \frac{1}{81} )}{ln ( x )} = 4

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{81} )}{ln ( x )} ln (x) = 4 ln (x)

Apply log rules

x = \frac{1}{3}

Verify Solutions:

x = \frac{1}{3}

True

The solution is

x = \frac{1}{3}

6 = ln (s)

9^{l o g_{3} (x)} = x - 2 x^{2} + 4

ln (3 x - 14) = 4

ln (3 x - 14) = 3

3 lo g_{10} (x) = 6