MATH SOLVE

2 months ago

Q:
# Solve the following equations.ln(x + 2) + ln(x − 2) = ln(9x − 24)

Accepted Solution

A:

Answer:x = 4 and, x = 5Step-by-step explanation:Data provided:ln(x + 2) + ln(x − 2) = ln(9x − 24) .............(1)Now,from the properties of natural log, we have ln(A) + ln(B) = ln(AB)applying the above property in the equation given, we getln(x + 2) + ln(x − 2) = ln((x + 2)(x - 2))orln(x + 2) + ln(x − 2) = ln(x² - 2²)on substituting the above result in the equation (1)ln(x² - 2²) = ln(9x − 24)taking the anti-log both sides, we get(x² - 2²) = (9x − 24)orx² - 4 = 9x - 24orx² - 4 - 9x + 24 = 0orx² - 9x + 20 = 0orx² - 4x - 5x + 20 = 0orx(x - 4) - 5(x - 4) = 0or(x - 4)(x - 5) = 0thus,x = 4 and, x = 5