1. 3.5 Equation Solving & Modeling

2. One-to-One Properties
For any exponential function f(x) = bx,
If bu = bv, then u = v
For any logarithmic function f(x) = logbx,
If logb u = logb v, then u = v

3. Find the exact solution algebraically

4. You Try! Find the exact solution algebraically
2(5)

5. Find the exact solution algebraically

6. You Try! Solve:

7. Solve:

8. You Try! Solve:

9. Solve: ln(x-3) + ln(x+4) = 3 ln 2

10. You Try! Solve: log(x-2) + log(x+5) = 2 log 3

11. Comparing Earthquakes: How many times more severe was the 1978 Mexico City earthquake (R = 7.9) than the 1994 Los Angeles (R= 6.6)?

12. Newton’s Law of Cooling
T(t) = Tm + (T0 – Tm)e-kt
Tm = the temperature of the surrounding medium
T0 = initial temperature of the object

13. Newton’s Law of Cooling: A cup of coffee has cooled from 920C to 500C after 12 minutes in a room at 220C. How long will the cup take to cool to 300C?