Question

If ${\left(\frac{5}{3}\right)}^{-5}\times {\left(\frac{5}{3}\right)}^{-11}={\left(\frac{5}{3}\right)}^{8x}$, then $x=?$

• A. $\frac{-1}{2}$
• B. $-2$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$-2$

Given, ${\left(\frac{5}{3}\right)}^{-5}\times {\left(\frac{5}{3}\right)}^{11}={\left(\frac{5}{3}\right)}^{8+x}$

LHS $=$ $(5/3{)}^{-5+11}=(5/3{)}^6$

On aomparing powers of RHS and LHS as the bases are same, we get

$8+x=6$

$\Rightarrow x=-2$