Checkpoint: Solve Logs with Properties Solution

Solve.

$\log_{4} (x + 2) - \log_{4} (x - 1) = 1$

$\begin{array}{rcl} \log_{4} \frac{x + 2}{x - 1} & = & 1 \\ 4^{1} & = & \frac{x + 2}{x - 1} \\ 4 (x - 1) & = & x + 2 \\ 4 x - 4 & = & x + 2 \\ 3 x & = & 6 \\ x & = & 2 \end{array}$

Check

$\log_{4} (2 + 2) - \log_{4} (2 - 1) = 1 ✓$

Note

Q: What property do you need to use to contract the left side of the equation? Explain.

A: When logs are subtracted, the quotient property is used.