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

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

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log_{x}(1/16)=2

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

x = \frac{1}{4}

Decimal Notation

x = 0.25

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 = \frac{1}{4}

Verify Solutions:

x = \frac{1}{4}

True

The solution is

x = \frac{1}{4}

ln (\frac{t - 67}{125}) = - 0.07 t

6 lo g_{10} (x) = 10

2 lo g_{3} (x) - lo g_{3} (x + 6) = 0

x, 3 ln (x) = 6

ln (x^{10}) = x