Solving Exponential Equations

What is to be learned? How to solve exponential equations

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

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

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

Solving Exponential Equations Equations where unknown is a power

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

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? 1000000 = 1000e0.2t 1000000 = 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

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