14
AssignmentMultiple Choice

Solving Equations using Properties of Logarithms

Question 14 • DHS Algebra 2 V

Which equation can you solve to find the potential solutions to the equation log2x + log2(x – 6) = 4?

Answer
A
x2 – 6x – 4 = 0
B
x2 – 6x – 8 = 0
C
x2 – 6x – 16 = 0

Explanation

Use the product rule for logarithms: log₂x + log₂(x − 6) = log₂[x(x − 6)]. Since this equals 4, the argument must equal 2⁴ = 16, so x(x − 6) = 16. Expanding and rearranging gives x² − 6x − 16 = 0, the equation in choice C.

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