Question

find the value of n 3^n*3^-5=3^2​

Answer 1

$\red{ The \: value \: of \: n \: in \: 3^{n} \times 3^{-5} }= 3^{2}$

$\implies 3^{n-5} = 3^{2}$

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By Exponential Law :

$\pink { a^{m} \times a^{n} = a^{m+n} }$

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$\implies n - 5 = 2$

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By Exponential Law :

$\blue { If\: a^{m} = a^{n} \implies m = n }$

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$\implies n = 2 + 5$

$\implies n = 7$

Therefore.,

$\red { Value \:of \:n } \green {= 7}$

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