Question

If $4^a+4^{a+1}=4^{a+2}-176$, what is the value of $a$?

• A. $2$
• B. $1$
• C. $3$
• D. $4$

Answer 1

Answer: (A)

$2$

The key to this problem is to express all of the exponential terms of the greatest common factor of the terms: $4^a$. Using the addition rule (or the corresponding numerical examples), we get

$4^a+4^{a+1}=4^{a+2}-176$

$176=4^{a+2}-4^a-4^{a+1}$

$176=4^a\times \left(4^2\right)-4^a-4^a.\left(4^1\right)$

$176=4^a\times (4^2-4^0-4^1)$

$176=4^a\times (16-1-4)$

$176=4^a\times \left(11\right)$

$4^a=176÷11=16$

$a=2$