What is the answer to log_{a}(216)=3 ?

The answer to log_{a}(216)=3 is a=6

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log_{a}(216)=3

lo g_{a} (216) = 3

a = 6

Solution steps

lo g_{a} (216) = 3

Apply log rules

\frac{1}{lo g _{216} ( a )} = 3

Multiply both sides by

lo g_{216} (a)

\frac{1}{lo g _{216} ( a )} lo g_{216} (a) = 3 lo g_{216} (a)

Simplify

1 = 3 lo g_{216} (a)

Switch sides

3 lo g_{216} (a) = 1

Divide both sides by

3

lo g_{216} (a) = \frac{1}{3}

Apply log rules

a = 6

Verify Solutions:

a = 6

True

The solution is

a = 6

lo g_{3} (11 - 4 x) = 3

lo g_{10} (3 x - 2) = 2

lo g_{2} (b) = - 5

lo g_{10} (x) + lo g_{10} (x + 21) = 2

lo g_{3} ((x^{2} + 2)^{2}) = 6