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Let $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be real numbers, each greater than 1 , such that $\frac{2}{3} \log _{\mathrm{b}} \mathrm{a}+\frac{3}{5} \log _{\mathrm{c}} \mathrm{b}+\frac{5}{2} \log _{\mathrm{a}} \mathrm{c}=3$. If the value of $b$ is 9 , then the value of ' $a$ ' must be
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27
$\frac{2 \ln a}{3 \ln b}+\frac{3 \ln b}{5 \ln c}+\frac{5 \ln c}{2 \ln a}=3$
By A.M $=$ G.M
$\frac{2 \ln a}{3 \ln b}=1$
$\Rightarrow a^{2}=b^{3} \Rightarrow a=\left(3^{6}\right)^{1 / 2}=3^{3} \Rightarrow a=27$
By A.M $=$ G.M
$\frac{2 \ln a}{3 \ln b}=1$
$\Rightarrow a^{2}=b^{3} \Rightarrow a=\left(3^{6}\right)^{1 / 2}=3^{3} \Rightarrow a=27$
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