Question

Janet solves this equation

log(x-3)+logx=1

She finds the two solutions; x=5 and x=-2

Of Janet’s two solutions, ____ correct because _____

A. Neither x=5 nor x=-2 is
B. Only x=5 is
C. Only x=-2 is
D. Both x=5 and x=-2 are

1. x=5 is an extraneous solution
2. Both x=-2 and x=5 are valid solutions
3. Both x=-2 and x=5 are extraneous solutions
4. x=-2 is an extraneous solution

(TWO DIFFERENT ANSWERS FILL IN THE BLANK)

Answer 1

Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions

Logarithmic function

Given the log function expressed as:

log(x-3) + logx=1

According to the law of logarithm, addition becomes product to have:

log x(x -3) = log₁₀10

x² - 3x = 10

x² - 3x -10 = 0
x² - 5x + 2x - 10 = 0
x(x-5) + 2(x-5) = 0
(x+2)(x-5)=0

x = -2 and 5

Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions

Learn more on logarithm here: https://brainly.com/question/25710806

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