Question

If $\frac{2^{m-3}}{4^{2m}}=8$, then $2m-1$ is equal to:

• A. $0$
• B. $1$
• C. $-5$
• D. $-9$

Answer 1

Answer: (C)

$-5$

Write $4^{2m}$ and $8$ in exponential form with exponent $2$ that is

$4^{2m}={\left(2^2\right)}^{2m}=2^{4m}$

$8=2^3$

Use the above in the given equation

$\frac{2^{m-3}}{2^{4m}}=2^3$

$\Rightarrow 2^{m-3-4m}=2^3$

$\Rightarrow m-3-4m=3$

$\Rightarrow -3m=6$

$\Rightarrow m=-2$

Therefore, $2m-1=2(-2)-1=-5$.

Hence option $C$ is correct.