How do you solve ${log}_{5} (5^{6 n + 1}) = 13$ $log_5(5^(6n+1))=13$ ?

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Answer 1 · 2016-10-24T02:27:56

$n = 2$ $n = 2$

${log}_{5} 5^{6 n + 1} = 13$ $log_5 5^(6n + 1) = 13$

${log}_{n} m^{x} = x {log}_{n} m$ $log_n m^x = x log_n m$

$\Rightarrow (6 n + 1) {log}_{5} 5 = 13$ $=> (6n + 1)log_5 5 = 13$

${log}_{n} n = 1$ $log_n n = 1$

$\Rightarrow 6 n + 1 = 13$ $=> 6n + 1 = 13$

$\Rightarrow 6 n = 12$ $=> 6n = 12$

$\Rightarrow n = 2$ $=> n = 2$

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