Lesson 13- Exponential Equations

In this lesson there are to different methods. Common base method, or the Log method

Method 1: Common Base

3^2x = 27^3x-1              1) Find Common Base
3^2x = (3^3)^ 3x-1
3^2x = 3^9x-3                2) Drop the Base
2x = 9x-3
3 = 7x                             3) Solve
3/7 = x

Check:  (put answer into original equation)
3^3/7 = 27^3(3/7) -1
2.55 = 2.55   
correct!!

Method 2: Logs

3^2x = 27^3x-1              1) log both sides
log3^2x = log27^3x-1
2xlog3 = (3x-1)log27            2) Factor out brackets
2xlog3= 3xlog27 - log27
2xlog3- 3xlog27= -log27        3) factor out x
x ( 2log3 - 3log27)  =      -log27                        4) Solve for x
    (2log3- 3log27)     (2log3- 3log27)
x= 0.42857
x= 3/7

*note: when using calculator, remember to use brackets or the answer may be wrong.