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If log3a2=3log3b, express a in terms of b....

If log3a2=3log3b, express a in terms of b.

A.

a=b33

B.

a=b39

C.

a=9b3

D.

a=b39

Correct answer is C

log3a2=3log3b

Using the laws of logarithm, we know that 2=2log33=log332

= \log_{3}(\frac{a}{3^{2}}) = \log_{3}b^{3}   \implies  \frac{a}{9} = b^{3}

\implies a = 9b^{3}