Question

Kim solved the equation below by graphing a system of equations.

log Subscript 2 Baseline (3 x minus 1) = log Subscript 4 Baseline (x + 8)

What is the approximate solution to the equation?
0.6
0.9
1.4
1.6

Answer 1

Solve by converting to base 2: log_4(x+8) = (1/2)log_2(x+8), so
log_2(3x−1) = (1/2)log_2(x+8) ⇒ 2log_2(3x−1) = log_2(x+8)
⇒ log_2((3x−1)^2) = log_2(x+8) ⇒ (3x−1)^2 = x+8.

Solve: 9x^2 − 6x +1 = x + 8 ⇒ 9x^2 −7x −7 = 0.
x = [7 ± √301]/18 ≈ 1.3527 or −0.5749. Domain requires x > 1/3, so x ≈ 1.35.

Closest choice: 1.4.