Question

Find $m$ such that $2^{m^2+8m-15}=4^{4m+5}$

• A. $5$
• B. $-5$
• C. $\pm 5$
• D. None of these

Answer 1

Answer: (C)

$\pm 5$

$2^{m^2+8m-15}={\left(2^2\right)}^{4m+5}$
$\therefore 2^{m^2+8m-15}=2^{8m+10}$
Comparing the powers
$\therefore m^2+8m-15=8m+10$
$\therefore m^2+8m-8m-15-10=0$
$\therefore m^2-25=0$
$\therefore m^2=25$
$\therefore m=\pm 5$