What is the answer to log_{a}(8)=3 ?

The answer to log_{a}(8)=3 is a=2

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log_{a}(8)=3

lo g_{a} (8) = 3

a = 2

Solution steps

lo g_{a} (8) = 3

Apply log rules

\frac{1}{lo g _{8} ( a )} = 3

Multiply both sides by

lo g_{8} (a)

\frac{1}{lo g _{8} ( a )} lo g_{8} (a) = 3 lo g_{8} (a)

Simplify

1 = 3 lo g_{8} (a)

Switch sides

3 lo g_{8} (a) = 1

Divide both sides by

3

lo g_{8} (a) = \frac{1}{3}

Apply log rules

a = 2

Verify Solutions:

a = 2

True

The solution is

a = 2

lo g_{4} (x) = \frac{- 3}{2}

lo g_{x} (4) = \frac{2}{3}

a, lo g_{a} (b) = 3

lo g_{x} (64) = 4

lo g_{6} (x) + lo g_{6} (x - 1) = 1