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

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

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log_{x}(1/9)=2

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

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

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 = \frac{1}{3}

Verify Solutions:

x = \frac{1}{3}

True

The solution is

x = \frac{1}{3}

\frac{ln ( 3 x - 1 )}{ln ( x - 1 )} = 3

lo g_{10} (x) + lo g_{10} (x + 48) = 2

lo g_{10} (x) - lo g_{10} (x - 3) = 2

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

x, y = 4 \cdot ln (x + c)