Question

For which value of $q,8^{-2q+3}=8^{-3q}?$

• A. $q=3$
• B. $q=1$
• C. $q=-3$
• D. $q=-1$

Answer 1

The correct option is C $q=-3$

$\underset{–}{\text{Need to find:}}$ Value of $q$ which satisfies the exponential equation $8^{-2q+3}=8^{-3q}$

$8^{-2q+3}=8^{-3q}$

In the above exponential equation, the base $\left(8\right)$ is same. Hence, for L.H.S=R.H.S, the powers must be same.

$\Rightarrow -2q+3=-3q$
$\Rightarrow -2q+3+3q=-3q+3q$
$\Rightarrow -2q+3q+3=0$
$\Rightarrow q+3=0$
$\Rightarrow q+3-3=0-3$
$\Rightarrow \underset{–}{q=-3}$

$\therefore$ The value of $q$ which satisfies the exponential equation $8^{-2q+3}=8^{-3q}$ is $\underset{–}{3}$.

Therefore, option (c.) is the correct one.