log_1/39√(3) =log_3^ 13^2+1/2 =log_3^ 13^5/2 We have log_a^na^m=mnlog_aa =5/2 1log_33 #160; since log_aa=1 = 52 ...

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Property 6

Solve: log1/...

Question

Solve: ${log}_{\frac{1}{3}} 9 \sqrt{3}$

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Solution

${log}_{\frac{1}{3}} 9 \sqrt{3}$

$= {log}_{3^{- 1}} 3^{2 + \frac{1}{2}}$

$= {log}_{3^{- 1}} 3^{\frac{5}{2}}$

We have ${log}_{a^{n}} a^{m} = \frac{m}{n} {log}_{a} a$

$= \frac{\frac{5}{2}}{- 1} {log}_{3} 3$ since ${log}_{a} a = 1$

$= \frac{- 5}{2}$

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