What is the answer to log_{x}(1/64)=-6 ?

The answer to log_{x}(1/64)=-6 is x=2

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log_{x}(1/64)=-6

lo g_{x} (\frac{1}{64}) = - 6

x = 2

Solution steps

lo g_{x} (\frac{1}{64}) = - 6

Apply log rules

\frac{ln ( \frac{1}{64} )}{ln ( x )} = - 6

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{64} )}{ln ( x )} ln (x) = - 6 ln (x)

Apply log rules

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

lo g_{t} (243) = 5

2 lo g_{4} (x) = 2

lo g_{9} (m) = - 2 + lo g_{9} (m - 4)

lo g_{10} (3 x - 8) = lo g_{10} (x + 6)

2 lo g_{10} (x) = - 3 lo g_{10} (2)