What is the answer to log_{x}(1/4)=-2 ?

The answer to log_{x}(1/4)=-2 is x=2

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log_{x}(1/4)=-2

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

x = 2

Solution steps

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

Apply log rules

\frac{ln ( \frac{1}{4} )}{ln ( x )} = - 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{4} )}{ln ( x )} ln (x) = - 2 ln (x)

Apply log rules

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

ln (x^{3} - 3) = 3 ln (x) - ln (3)

- lo g_{10} (x) = 4

lo g_{2} (x - 6) + lo g_{2} (x + 1) = 3

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

lo g_{8} (x) = - 2