Question

Solve for solution set $(x,y):x^{y-1}:x^{y-2}=4$ and $x^{2y-3}=64$

Find $x-y$.

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

1

We have been given that $\frac{x^{y-1}}{x^{y-2}}=4$

$\Rightarrow$ $\frac{\frac{x^y}{x^1}}{\frac{x^y}{x^2}}=4$ $[a^{m-n}=\frac{a^m}{a^n}]$

$\Rightarrow$ $\frac{x^y}{x^1}\times \frac{x^2}{x^y}=4$

$\therefore$ $x=4$ ----- ( 1 )

Also, $x^{2y-3}=64$

$\Rightarrow$ $4^{2y-3}=4^3$ ...[Substituting value of $x$]

$\Rightarrow$ $\frac{4^{2y}}{4^3}=4^3$

$\Rightarrow$ $4^{2y}=4^6$

$\Rightarrow$ $2y=6$

$\therefore$ $y=3$ ------ ( 2 )

$\therefore$ $x-y=4-3=1$ ...[From ( 1 ) and ( 2)]