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

The answer to log_{a}(9)=(2) is a=3

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log_{a}(9)=(2)

lo g_{a} (9) = (2)

a = 3

Solution steps

lo g_{a} (9) = (2)

Apply log rules

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

Multiply both sides by

lo g_{9} (a)

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

Simplify

1 = 2 lo g_{9} (a)

Switch sides

2 lo g_{9} (a) = 1

Divide both sides by

2

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

Apply log rules

a = 3

Verify Solutions:

a = 3

True

The solution is

a = 3

lo g_{\frac{1}{2}} (x - 3) = - 3

2 ln (x) - 3 = 0

ln (x^{2}) - 1 = 0

ln (2 x) - ln (x + 1) = ln (x - 5)

ln (x^{8} - 5) = 3