What is the answer to log_{x}(1/64)=2 ?

The answer to log_{x}(1/64)=2 is x= 1/8

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log_{x}(1/64)=2

lo g_{x} (\frac{1}{64}) = 2

x = \frac{1}{8}

Decimal Notation

x = 0.125

Solution steps

lo g_{x} (\frac{1}{64}) = 2

Apply log rules

\frac{ln ( \frac{1}{64} )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{64} )}{ln ( x )} ln (x) = 2 ln (x)

Apply log rules

x = \frac{1}{8}

Verify Solutions:

x = \frac{1}{8}

True

The solution is

x = \frac{1}{8}

lo g_{10} (x) = - 4138

1 = ln (x - 2)

lo g_{7} (4 x + 30) = lo g_{7} (72)

- 2 lo g_{x} (\frac{1}{100}) = 4

lo g_{5} (3 x + 1) + lo g_{5} (x - 3) = 3