What is the answer to log_{x}(1/36)=2 ?

The answer to log_{x}(1/36)=2 is x= 1/6

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log_{x}(1/36)=2

lo g_{x} (\frac{1}{36}) = 2

x = \frac{1}{6}

Decimal Notation

x = 0.16666 \dots

Solution steps

lo g_{x} (\frac{1}{36}) = 2

Apply log rules

\frac{ln ( \frac{1}{36} )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{36} )}{ln ( x )} ln (x) = 2 ln (x)

Apply log rules

x = \frac{1}{6}

Verify Solutions:

x = \frac{1}{6}

True

The solution is

x = \frac{1}{6}

y, ln (y) = 4 x + 3

ln (ln (x)) = ln (ln (x))

8 ln (6 - x) = 7

lo g_{x} (\frac{1}{7}) = - 1

lo g_{5} (x + 8) = - lo g_{5} (x + 4) + 1