Question

$If{81}^y=\frac{1}{{27}^x},intermsofy,x=?$

• A. $\frac{3y}{4}$
• B. $-\frac{3y}{4}$
• C. $\frac{4y}{3}$
• D. $-\frac{4y}{3}$

Answer 1

The correct option is D $-\frac{4y}{3}$

${81}^y=\frac{1}{{27}^x}$

$\Rightarrow (3{)}^{4y}=(3^{-3}{)}^x$

$\Rightarrow (3{)}^{4y}=(3{)}^{-3x}$

as $a^m=a^n$

and $a\ne -1,0,+1$

$\Rightarrow m=n$

so 4y = -3x

$x=-\frac{4}{3}y$