Target Test Prep Sample Problem Solving Problem

Solution:

To determine the value of x, we must get like bases. We can prime factorize each base. Once the bases are the same, we can set the exponents equal to each other.

⇒ 24⁴ × 16^x+3 = 18²

⇒ (3×2³)⁴ × (2⁴)^x+3 = (3² × 2¹)²

⇒ 3⁴ × 2¹² × 2^4x+12 = 3⁴ × 2²

The 3⁴ on the left hand side of the equation and on the right hand side of the equation cancel out and we are left with:

⇒ 2¹² × 2^4x+12 = 2²

⇒ 2^4x+24 = 2²

Since the bases are equal we can drop the bases and determine the value of x.

⇒ 4x + 24 = 2

⇒ 4x = -22

⇒ x = $-\frac{22}{4}=-\frac{11}{2}=-5.5$