Question

If $4^x+4^x+4^x+4^x+4^x+4^x+4^x+4^x=\frac{1}{512}$, what is the value of $\frac{-3}{x}$?

• A. $0.50$
• B. $0.75$
• C. $-0.75$
• D. $-4.25$

Answer 1

Answer: (A)

$0.50$

$Now{4}^x+4^x+4^x+4^x+4^x+4^x+4^x+4^x=\frac{1}{512}\to 4^x(1+1+1+1+1+1+1+1)=\frac{1}{2^9}\to 4^x\left(8\right)=2^{-9}\to 2^{2x}\left(2^3\right)=2^{-9}\to 2^{2x+3}=2^{-9}$

Equating powers, we get

$\to 2x+3=-9\to 2x=-9-3\to 2x=-12\to x=\frac{-12}{2}\to x=-6Now\frac{-3}{x}=\frac{-3}{-6}=\frac{1}{2}=0.50$