Lesson # 13: Exponential Equations

In this lesson there are 2 different methods to find x: Common Bases method, or the Log method

Method 1- Common Bases:

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:
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*