What is the answer to log_{a}(16)=4 ?

The answer to log_{a}(16)=4 is a=2

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log_{a}(16)=4

lo g_{a} (16) = 4

a = 2

Solution steps

lo g_{a} (16) = 4

Apply log rules

\frac{1}{lo g _{16} ( a )} = 4

Multiply both sides by

lo g_{16} (a)

\frac{1}{lo g _{16} ( a )} lo g_{16} (a) = 4 lo g_{16} (a)

Simplify

1 = 4 lo g_{16} (a)

Switch sides

4 lo g_{16} (a) = 1

Divide both sides by

4

lo g_{16} (a) = \frac{1}{4}

Apply log rules

a = 2

Verify Solutions:

a = 2

True

The solution is

a = 2

20 lo g_{10} (x) = 80

lo g_{3} (x) = lo g_{3} (6)

lo g_{x} (2 x^{2} - 8 x + 15) = 2

0 = 1 - ln (x - 1)

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