What is the answer to log_{a}(36)=2 ?

The answer to log_{a}(36)=2 is a=6

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log_{a}(36)=2

lo g_{a} (36) = 2

a = 6

Solution steps

lo g_{a} (36) = 2

Apply log rules

\frac{1}{lo g _{36} ( a )} = 2

Multiply both sides by

lo g_{36} (a)

\frac{1}{lo g _{36} ( a )} lo g_{36} (a) = 2 lo g_{36} (a)

Simplify

1 = 2 lo g_{36} (a)

Switch sides

2 lo g_{36} (a) = 1

Divide both sides by

2

lo g_{36} (a) = \frac{1}{2}

Apply log rules

a = 6

Verify Solutions:

a = 6

True

The solution is

a = 6

lo g_{10} (x) + y (3) = 2

x, ln (v) = - ln (x)

lo g_{10} (x) = 10 + lo g_{10} (4)

lo g_{2} (x) = \frac{1}{3}

0 = - lo g_{10} (x) + 2