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

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

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log_{x}(1/64)=-2

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

x = 8

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 = 8

Verify Solutions:

x = 8

True

The solution is

x = 8

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

lo g_{6} ((5 x - 9)^{2}) = 4

lo g_{x} (5) = 3

x, ln (x) - ln (x + 2) = 1

ln (x) = 0.66