1. Solving Exponential Equations

2. What is to be learned?
How to solve exponential equations

3. Exponential Equation? Equation where power is unknown 5x = 125 x = 3
(General Knowledge)
(Trial and error)
need a better tactic

4. The Log Tactic 8x = 900 neat wee tactic log 8 = log 900 x = log 900

5. A bit nastier 15 X 3x = 3000 3x = 3000 3x = 200 15 log 3x = log 200
x log 3 = log 200
x = log 200
x = 4.82 15
log 3

6. Solving Exponential Equations
Equations where unknown is a power

7. 30 X 6x = 1200
Eliminate 30
6x = 1200
6x = 40
Logs on both Sides
Log 6x = log 40
Neat wee tactic
x log 6 = log 40
x = log 40 30
(using log10)
= 2.06
log 6

8. Natural Growth Population of some sort of creepy crawlie P = P0e0.2t
If there are 1000 ccs to start with, how long will it take to reach a million?
= 1000e0.2t
= e0.2t
1000 = e0.2t
ln 1000 = ln e0.2t
ln 1000 = 0.2t ln e
P is Population over t days P0 P
ln 1000 = 0.2t
1000
t = ln 1000
0.2
= 34.5 days
= 1

9. When e is involved using ln is a neat tactic
Tina’s tea temperature (T 0C) after t mins
T = T0e-0.2t
How long until it is half its initial temp?
T = e-0.2t
0.5 = e-0.2t
ln 0.5 = ln e-0.2t
ln 0.5 = -0.2t ln e
ln 0.5 = -0.2t
t = ln 0.5 T0
= 1
= 3.5 mins
-0.2