What is the answer to log_{x}(1/81)=2 ?

The answer to log_{x}(1/81)=2 is x= 1/9

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log_{x}(1/81)=2

lo g_{x} (\frac{1}{81}) = 2

x = \frac{1}{9}

Decimal Notation

x = 0.11111 \dots

Solution steps

lo g_{x} (\frac{1}{81}) = 2

Apply log rules

\frac{ln ( \frac{1}{81} )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{81} )}{ln ( x )} ln (x) = 2 ln (x)

Apply log rules

x = \frac{1}{9}

Verify Solutions:

x = \frac{1}{9}

True

The solution is

x = \frac{1}{9}

lo g_{2} (3 x) = 10

lo g_{6 x + 1} (2) = 1

5 ln (b - 9) = 20

lo g_{4} (x) + 3 lo g_{2} (x) = 7

lo g_{12} (y) = 4