57
QuizMultiple Choice

N/A — Exam

Question 57 • Algebra II

Consider the equation. log sub 4 of open paren x plus 3 close paren is equal to log sub 2 of open paren 2 plus x close paren Which system of equations can represent the equation?

Answer
A
y sub 1 is equal to the fraction with numerator log x plus 3 and denominator 4 , y sub 2 is equal to the fraction with numerator log 2 plus x and denominator 2
B
y sub 1 is equal to the fraction with numerator the log of open paren x plus 3 close paren and denominator log 4 , y sub 2 is equal to the fraction with numerator the log of open paren 2 plus x close paren and denominator log 2
C
y sub 1 is equal to the fraction with numerator log 4 and denominator log 2 , y sub 2 is equal to the log of open paren x plus 3 close paren over the log of open paren 2 plus x close paren
D
y sub 1 is equal to the fraction with numerator log x plus 3 and denominator log 4 , y sub 2 is equal to the fraction with numerator log 2 plus x and denominator log 2

Explanation

Using the change-of-base formula, log base b of a number a equals log(a) divided by log(b). Thus the left side is log(x + 3)/log(4), and the right side is log(2 + x)/log(2). Setting y₁ and y₂ equal to these expressions represents the original equation as the intersection condition y₁ = y₂, matching choice B.

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