Question

Solve. Check for extraneous solutions.
1. In(4x + 1) = ln(2x + 5)

Answer 1

The answer is x = 2. No extraneous solutions.

Explanation:

Raise both sides to the eth power:

4x + 1 = 2x + 5

2x + 1 = 5

2x = 4

x = 2

We plug this in:

ln(4(2)+1) = ln(8 + 1) = ln(9)

ln(2(2) + 5) = ln(4 + 5) = ln(9)