Question

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

log Subscript 3 Baseline 5 x = log Subscript 5 Baseline (2 x + 8)

Which point approximates the solution for Tenisha’s system of equations?
(0.9, 0.8)
(1.0, 1.4)
(2.3, 1.1)
(2.7, 13.3)

Answer 1

Interpret the system as y = log_3(5x) and y = log_5(2x+8). Check the candidates by plugging in x and comparing the y-values.

For (1.0, 1.4):
- log_3(5·1) = ln5 / ln3 ≈ 1.6094 / 1.0986 ≈ 1.465
- log_5(2·1+8) = ln10 / ln5 ≈ 2.3026 / 1.6094 ≈ 1.431

Both are about 1.4, so (1.0, 1.4) is the intersection.

Answer: (1.0, 1.4).