Question

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

Answer 1

x = 4 and, x = 5

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 get

ln(x + 2) + ln(x − 2) = ln((x + 2)(x - 2))

or

ln(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)

or

x² - 4 = 9x - 24

or

x² - 4 - 9x + 24 = 0

or

x² - 9x + 20 = 0

or

x² - 4x - 5x + 20 = 0

or

x(x - 4) - 5(x - 4) = 0

or

(x - 4)(x - 5) = 0

thus,

x = 4 and, x = 5