Question

1. what real value of ( x ) satisfies the equation ( \frac{2^{4x + 3}}{2^{2x}} = 128 )

a. ( \frac{3}{2} )
b. 1
c. 2
d. 4

Explanation:

Step1: Simplify left-hand side

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$:
$\frac{2^{4x+3}}{2^{2x}} = 2^{(4x+3)-2x} = 2^{2x+3}$

Step2: Rewrite right-hand side as power of 2

$128 = 2^7$

Step3: Set exponents equal

Since bases are equal, equate exponents:
$2x + 3 = 7$

Step4: Solve for x

Subtract 3, then divide by 2:
$2x = 7 - 3 = 4$
$x = \frac{4}{2} = 2$

Answer:

C. 2