Select-the-correct-option-with-explaination-If-1-3-log-3-M-3log-3-N-1-log-0-008-5-then-a-M-9-9-N-b-N-9-9-M-c-M-3-3-N-d-N-3-3-M-

Question Number 193253 by MATHEMATICSAM last updated on 08/Jun/23

Select the correct option with

explaination :

If \frac{1}{3} \log_{3} M + {3 \log}_{3} N = 1 + \log_{0.008} 5 then

a . M^{9} = \frac{9}{N}

b . N^{9} = \frac{9}{M}

c . M^{3} = \frac{3}{N}

d . N^{3} = \frac{3}{M}

Answered by AST last updated on 08/Jun/23

{l o g}_{3} {({M N}^{9})}^{\frac{1}{3}} = 1 + x

{l o g}_{0.008} 5 = x \Rightarrow {(5^{- 3})}^{x} = 5 \Rightarrow x = - \frac{1}{3}

\Rightarrow 3^{\frac{2}{3}} = {({M N}^{9})}^{\frac{1}{3}} \Rightarrow 9 = {M N}^{9} \Rightarrow N^{9} = \frac{9}{M}

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