What is the answer to log_{x}(1/16)=-2 ?

The answer to log_{x}(1/16)=-2 is x=4

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log_{x}(1/16)=-2

lo g_{x} (\frac{1}{16}) = - 2

x = 4

Solution steps

lo g_{x} (\frac{1}{16}) = - 2

Apply log rules

\frac{ln ( \frac{1}{16} )}{ln ( x )} = - 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{16} )}{ln ( x )} ln (x) = - 2 ln (x)

Apply log rules

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

\frac{1 - ln ( x )}{x ^{2}} = 0

lo g_{10} (16 x) - lo g_{10} (4) = 2

lo g_{3} (x^{2} - 5 x + 3) = 2

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

e^{x l n (x)} = x^{2}