What is the answer to log_{a}(64)=3 ?

The answer to log_{a}(64)=3 is a=4

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log_{a}(64)=3

lo g_{a} (64) = 3

a = 4

Solution steps

lo g_{a} (64) = 3

Apply log rules

\frac{1}{lo g _{64} ( a )} = 3

Multiply both sides by

lo g_{64} (a)

\frac{1}{lo g _{64} ( a )} lo g_{64} (a) = 3 lo g_{64} (a)

Simplify

1 = 3 lo g_{64} (a)

Switch sides

3 lo g_{64} (a) = 1

Divide both sides by

3

lo g_{64} (a) = \frac{1}{3}

Apply log rules

a = 4

Verify Solutions:

a = 4

True

The solution is

a = 4

ln (- x - 5) = ln (x - 61) - ln (x + 7)

ln (5 x + e) = - 8

lo g_{3} (\frac{6 x + 7}{x + 2} - 1) = 0

lo g_{4} ((x + 1)^{6}) = 12

lo g_{10} (n) = lo g_{10} (n)