Question

ccsd pre - calculus cp ic 25 - 26 solving equations using properties of logarithms solving when one term is a constant which of the following equations is equivalent to 2log₄x−log₄9 = 2? log₄(\frac{x}{9}) = 2 log₄(x²−9) = 2 log₄(\frac{x}{9}) = 2

Explanation:

Step1: Use logarithm properties

Recall that \(n\log_aM=\log_aM^n\) and \(\log_aM-\log_aN = \log_a\frac{M}{N}\). So, \(2\log_4x-\log_49=\log_4x^2-\log_49=\log_4\frac{x^2}{9}\).

Step2: Compare with given equations

We want to find which equation is equivalent to \(2\log_4x - \log_49=2\). Since \(2\log_4x-\log_49=\log_4\frac{x^2}{9}\), the equivalent equation is \(\log_4(\frac{x^2}{9}) = 2\).

Answer:

\(\log_4(\frac{x^2}{9}) = 2\)