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

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

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log_{x}(1/4)=2

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

x = \frac{1}{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 = \frac{1}{2}

Verify Solutions:

x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

lo g_{3} (x^{2} + 17) = 2

lo g_{3} (x) = lo g_{x} (27) + 2

ln (x^{2} - 9) = 0

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

lo g_{2} (x + 1) = 4