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

The answer to log_{b}(36)=-2 is b= 1/6

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log_{b}(36)=-2

lo g_{b} (36) = - 2

b = \frac{1}{6}

Decimal Notation

b = 0.16666 \dots

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 = \frac{1}{6}

Verify Solutions:

b = \frac{1}{6}

True

The solution is

b = \frac{1}{6}

lo g_{10} (x) + lo g_{10} (x + 9) = 2

lo g_{8} (x + 6) = \frac{2}{3}

0.88 = ln (x)

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

lo g_{9} (x) = (lo g_{3} (x)) 2