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algebra senior

Problem

If

a = lo g_{8} 225

and

b = lo g_{2} 15

, then

a

, in terms of

b

, is:

(A)

\frac{b}{2}

(B)

\frac{2 b}{3}

(C)

b

(D)

\frac{3 b}{2}

Solution

Using the change-of-base rule:

a = \frac{l o g 225}{l o g 8}

and

b = \frac{l o g 15}{l o g 2}

.

\frac{a}{b} = \frac{lo g 225 lo g 2}{lo g 8 lo g 15}

a = b \cdot \frac{lo g 225}{lo g 15} \cdot \frac{lo g 2}{lo g 8}

a = b lo g_{15} 225 lo g_{8} 2

a = \frac{2 b}{3}

Final answer

B