What is the answer to log_{b}(32)= 5/6 ?

The answer to log_{b}(32)= 5/6 is b=64

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log_{b}(32)= 5/6

lo g_{b} (32) = \frac{5}{6}

b = 64

Solution steps

lo g_{b} (32) = \frac{5}{6}

Apply log rules

\frac{1}{lo g _{32} ( b )} = \frac{5}{6}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 6 = lo g_{32} (b) \cdot 5

Simplify

6 = lo g_{32} (b) \cdot 5

Switch sides

lo g_{32} (b) \cdot 5 = 6

Divide both sides by

5

lo g_{32} (b) = \frac{6}{5}

Apply log rules

b = 64

Verify Solutions:

b = 64

True

The solution is

b = 64

lo g_{2} (x) + lo g_{2} (2 x - 3) = 1

2 lo g_{3} (x) - 3 = 0

ln (x - 5) = - 1

lo g_{a} (729) = 3

lo g_{2} (y) = 0