AnswersMathematics IIIPractice TestQuestion 20
20
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Practice Test

Question 20 • Mathematics III

Which of the following shows the true solution to the logarithmic equation solved? log sub 2 of x plus log sub 2 of open paren x plus 7 close paren is equal to 3 log sub 2 of open bracket x times open paren x plus 7 close paren close bracket is equal to 3 x times open paren x plus 7 close paren is equal to 2 cubed x squared plus 7 x minus 8 is equal to 0 open paren x plus 8 close paren times open paren x minus 1 close paren is equal to 0 x is equal to negative 8 comma 1

Answer
A
x is equal to negative 8
B
x is equal to 1
C
x is equal to 1 and x is equal to 8
D
x is equal to 1 and x is equal to negative 8

Explanation

The logarithms require x > 0 and x + 7 > 0, so x must be positive. Combining the logs gives log₂[x(x + 7)] = 3, hence x(x + 7) = 2³ = 8. Solving x² + 7x − 8 = 0 gives x = 1 or x = −8, but −8 is outside the domain; the true solution is x = 1, choice A.

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