What is the answer to log_{x}(1/9)=-2 ?

The answer to log_{x}(1/9)=-2 is x=3

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log_{x}(1/9)=-2

lo g_{x} (\frac{1}{9}) = - 2

x = 3

Solution steps

lo g_{x} (\frac{1}{9}) = - 2

Apply log rules

\frac{ln ( \frac{1}{9} )}{ln ( x )} = - 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{9} )}{ln ( x )} ln (x) = - 2 ln (x)

Apply log rules

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

lo g_{3} (x) - 4 lo g_{x} (3) + 3 = 0

2 lo g_{10} (x - 1) = lo g_{10} (2 x)

lo g_{x} (625) = 4

ln (6) + ln (x) - ln (2) = 3

lo g_{3} (4 x - 5) = lo g_{3} (2 x + 1)