Question

Which of the following shows extraneous solutions to the logarithmic equation? (See picture)

Answer 1

Option 3

Explanation:

log4(x) + log4(x - 3) = log4(-7x + 21)

log4(x² - 3x) = log4(-7x + 21)

x² - 3x = -7x + 21

x² + 4x - 21 = 0

x² + 7x - 3x - 21 = 0

x(x + 7) - 3(x + 7) =0

(x + 7)(x - 3) = 0

x = -7, 3

-7 and 3, both are e extraneous solutions because logs of non-positive numbers don't exist

At x = 3,

-7x + 21 = 0