What is the answer to log_{a}(64)=6 ?

The answer to log_{a}(64)=6 is a=2

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log_{a}(64)=6

lo g_{a} (64) = 6

a = 2

Solution steps

lo g_{a} (64) = 6

Apply log rules

\frac{1}{lo g _{64} ( a )} = 6

Multiply both sides by

lo g_{64} (a)

\frac{1}{lo g _{64} ( a )} lo g_{64} (a) = 6 lo g_{64} (a)

Simplify

1 = 6 lo g_{64} (a)

Switch sides

6 lo g_{64} (a) = 1

Divide both sides by

6

lo g_{64} (a) = \frac{1}{6}

Apply log rules

a = 2

Verify Solutions:

a = 2

True

The solution is

a = 2

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

lo g_{2} (4 x - 9) = 1

lo g_{2} (x) - lo g_{4} (2 x - 1) = 1

x, ln (y) + y = x + ln (x) + c

lo g_{2} (3 x - 2) = 1 + lo g_{2} (5)