What is the answer to log_{a}(64)=2 ?

The answer to log_{a}(64)=2 is a=8

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log_{a}(64)=2

lo g_{a} (64) = 2

a = 8

Solution steps

lo g_{a} (64) = 2

Apply log rules

\frac{1}{lo g _{64} ( a )} = 2

Multiply both sides by

lo g_{64} (a)

\frac{1}{lo g _{64} ( a )} lo g_{64} (a) = 2 lo g_{64} (a)

Simplify

1 = 2 lo g_{64} (a)

Switch sides

2 lo g_{64} (a) = 1

Divide both sides by

2

lo g_{64} (a) = \frac{1}{2}

Apply log rules

a = 8

Verify Solutions:

a = 8

True

The solution is

a = 8

lo g_{9} (2 x - 7) = \frac{3}{2}

3 lo g_{8} (x) - lo g_{x} (64 + 1) = 0

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

ln (4 x) + 1 = 0

lo g_{y} (125) = - \frac{3}{2}