Question

log (x+2)+log(x-2)=log3+3log4

Answer 1

logx + log2 + logx -log2 = log3 + log4

2logx = log3 + log4

hope it helps!

Answer 2

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log (x+2)+log(x-2)=log3+3log4

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$We \: know \: that, \\ log m + log n = logmn. \\ and \\ n \: log \: m = log m^n \\ Now, \\ \begin{gathered} log (x+2) + log (x-2) = log 3 + 3 log 4 \\ \\ log (x+2) (x-2) = log 3 + log 4 ^{3} \\ \\ log (x ^{2 } - 4 ) = log( 3 \times 4 ^{3} ) \\ \\ {x}^{2} - 4 = 192 \\ \\ {x}^{2} = 196 \\ \\ x = ±14\end{gathered}$

$\boxed{I \:Hope\: it's \:Helpful}$

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