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

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

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log_{x}(9)=-2

lo g_{x} (9) = - 2

x = \frac{1}{3}

Solution steps

lo g_{x} (9) = - 2

Apply log rules

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

Multiply both sides by

lo g_{9} (x)

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

Simplify

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

Switch sides

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

Divide both sides by

- 2

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

Apply log rules

x = \frac{1}{3}

Verify Solutions:

x = \frac{1}{3}

True

The solution is

x = \frac{1}{3}

lo g_{2} (x) + lo g_{2} (x - 6) = 4

ln (x^{2}) = 10

ln (x + 1) - ln (x) = 1

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

lo g_{3} (2 x + 1) = 2 + lo g_{3} (x - 9)