Question

Solve 36(3)^x=4 what is the value of x. include an explanation of how you got your answer

Answer 1

`\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^(-m)\implies a^(n-m) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 36(3)^x=4\implies 36(3^x)=4\implies 3^x=\cfrac{4}{36}\implies 3^x=\cfrac{1}{9} \\\\\\ 3^x=\cfrac{1}{3^2}\implies \stackrel{\textit{same bases, same exponents}}{3^x=3^(-2)}\implies x = -2`