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

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

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log_{b}(36)=2

lo g_{b} (36) = 2

b = 6

Solution steps

lo g_{b} (36) = 2

Apply log rules

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

Multiply both sides by

lo g_{36} (b)

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

Simplify

1 = 2 lo g_{36} (b)

Switch sides

2 lo g_{36} (b) = 1

Divide both sides by

2

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

Apply log rules

b = 6

Verify Solutions:

b = 6

True

The solution is

b = 6

lo g_{x + 3} (2 x^{2} - 5 x + 9) = 2

6 + 5 ln (x) = 3

lo g_{2} (x) = lo g_{8} (15)

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

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