Algebra 2 / Unit 5: Exponential and Logarithmic Functions
5.6 Solving Logarithmic Equations
Notes
- Isolate a single log, then rewrite in exponential form: $\log_b x = c \Rightarrow x = b^c$.
- Combine several logs into one with the properties first.
- Check answers: the input of every log must be positive, so some answers are extraneous.
- Example: $\log_2 (x + 1) = 3 \Rightarrow x + 1 = 8 \Rightarrow x = 7$.
Practice
Solve $\log_3 (x - 2) = 4$.
$x - 2 = 3^4 = 81$.
Solve $\log x + \log(x - 3) = 1$.
$x(x - 3) = 10 \Rightarrow (x - 5)(x + 2) = 0$. $x = -2$ makes $\log x$ undefined.
Solve $\ln x = 2$.
$\ln x = 2$ means $e^2 = x$.
Ready for more? Take the Unit 5 test.