http://www.ck12.org Chapter 3. Logs and Exponents
3.6 Exponential Equations
Here you will apply the new algebraic techniques associated with logs to solve equations.
When you were first learning equations, you learned the rule that whatever you do to one side of an equation, you
must also do to the other side so that the equation stays in balance. The basic techniques of adding, subtracting,
multiplying and dividing both sides of an equation worked to solve almost all equations up until now. With
logarithms, you have more tools to isolate a variable. Consider the following equation and ask yourself: why
isx=3? Logically it makes sense that if the bases match, then the exponents must match as well, but how can it be
shown?
1. 798982 x= 1. 798986Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61002http://www.youtube.com/watch?v=5R5mKpLsfYg James Sousa: Solving Exponential Equations II
Guidance
A common technique for solving equations with unknown variables in exponents is to take the log of the desired
base of both sides of the equation. Then, you can use properties of logs to simplify and solve the equation. See the
examples below.
Example A
Solve the following equation fort. Note: This type of equation is common in financial mathematics. This example
represents the unknown amount of time it will take you to save $9,000 in a savings account if you save $300 at the
end of each year in an account that earns 6% annual compound interest.
9 , 000 = 300 ·(^1.^060. 06 )tâ^1
Solution: