Question

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

Answer 1

Answer:

c

Step-by-step explanation:

Given the logarithmic equation

First, notice that

So, there is no possible solutions, all possible solutions will be extraneous.

Solve the equation:

then

Hence,  and  are extraneous solutions

Answer 2

Answer:

Option 3

Step-by-step 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