Exponential and Logarithmic Equations and Inequalities

about 30 min · 6 short parts · stop after any part

Questions like *"when will my money reach at least $10,000?"* are inequalities with exponents or logs.
By the end you can solve them, and you can undo (invert) any exp or log function.

The path

1
Warm-up: the tools you need
You can switch log ↔ exponent, find where a log exists, and combine logs.
2
Exponential inequalities (nice powers)
You can solve $3^{x+2} - 4 > 23$ .
3
When the power isn't nice
You can solve $3^x < 50$ and money problems with $A = Pe^{rt}$ .
4
Log inequalities: one log
You can solve $\log_2(2x+6) > 3$ , domain included.
5
Log inequalities: logs on both sides
You can solve $\log(x-8) + \log 2 \le \log(3x+4)$ .
6
Inverses: undo exp and log
You can find the inverse of $f(x) = 3(2^{x+1}) - 4$ .