Question

If $\frac{a^x}{a^y}=a^{10}$ and ${\left(a^y\right)}^3=a^x$ and $a>1$, then find the value of $x$.

• A. 5
• B. 10
• C. 15
• D. 20

Answer 1

The correct option is C 15

Given, $\frac{a^x}{a^y}=a^{10}$

The identity says $\frac{a^x}{a^y}=a^{x-y}$

Equating the two, gives $x-y=10...\left(1\right)$

The second condition, $(a^y{)}^3=a^{3y}=a^x$

$\Rightarrow 3y=x...\left(2\right)$

Using equations (1) and (2), we have

$3y-y=10$

$\to 2y=10$

$\to y=5$

$\therefore x=3y=15$