Question

Solve for x:what is x?

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Answer 1

x = —7

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Answer 2

`~\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}`

`8^x\cdot \cfrac{1}{4^(x-1)}=\cfrac{1}{32}\implies 8^x\cdot \cfrac{1}{4^x4^(-1)}=\cfrac{1}{32}\implies \cfrac{8^x}{4^x4^(-1)}=\cfrac{1}{32} \implies \cfrac{8^x}{4^x}\cdot \cfrac{1}{4^(-1)}=\cfrac{1}{32} \\\\\\ \left( \cfrac{8}{4} \right)^x\cdot 4=\cfrac{1}{32}\implies 2^x\cdot 2^2=\cfrac{1}{32}\implies 2^x\cdot 2^2=\cfrac{1}{2^5}\implies 2^(x+2)=2^(-5) \\\\\\ x+2=-5\implies x=-7`