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Evaluate (log_{3}9 - log_{2}8)/log_{3}9

A. -1/3

B. 1/2

C. 1/3

D. -1/2

**Comments**

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first, simplify

log_{3}9 = log_{3}3^{2} = 2log_{3}3

since, log_{a}b = (log_{10}b)/(log_{10}a)

similarly, log_{a}a = (log_{10}a)/(log_{10}a) = 1

Therefore, log_{3}3 = (log_{10}3)/(log_{10}3) = 1

**log _{3}9 =2(1) = 2**

log_{2}8 = log_{2}2^{3} = 3log_{2}2

log_{2}2 = 1

**log _{2}8 = 3(1) = 3**

(log_{3}9 - log_{2}8)/(log_{3}9) = (2 - 3)/2

= -1/2

**Ans D**

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