find the x-intercept of a natural log function

Question

find the x-intercept of the function y = ln(3x-2)^2.

in order to find it, move the power 2 in front of the natural log. y = 2 ln(3x-2).

for x -intercept, y = 0. Therefore, ln(3x-2) = 0. Hence, (3x-2) = 1. and x = 1.

The question is why cannot set (3x-2)^2 = 1. This give an additional answer (x = 1/3), which is wrong. Why?

Answer 1

Hi Sam,

Good question, even though x=1/3 makes 3x-2=-1 the ln(z) function is defined for z>0 this solution must be rejected .

Jim