Question

7log5(x+27)=14 What does X equal

Answer 1

$\bf \textit{Logarithm Cancellation Rules}\\\\log_a a^x = x\qquad \qquad \stackrel{\stackrel{\textit{we'll use this one}}{\downarrow }}{a^{log_a x}=x}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\7log_5(x+27)=14\implies log_5(x+27)=\cfrac{14}{7}\implies log_5(x+27)=2\\\\\\5^{log_5(x+27)}=5^2\implies x+27=5^2\implies x+27=25\implies x=-2$