4­5 Exponential and Logarithmic Equations and Inequalities
Objectives:
­ Solve exponential and logarithmic equations and inequalities. ­ Solve problems involving exponential and logarithmic equations. Who uses this?
Exponential scales are used to measure light in photography. 1
An exponential equation is an equation containing one or more expressions that have a variable as an exponent. A couple of methods to use to solve exponential equations...
• Try writing them so that the bases are all the same.
If
, then
• Take the logarithm of both sides. If
, then
2
Ex. Solve and check.
a.
b. 3
Try These
Ex. Solve and check.
a.
b.
c. 4
Ex. You can choose a prize of either $20,000 or one penny on the first day, double that (2 cents) on the second day, and so on for a month. On what day would you receive more than the value of the car?
$20,000 ⇒? cents
On day 1, you would receive 1 cent, or 20 cents. On day 2, you would receive 2 cents or 21. So, on day n you would receive ....?
5
Try These:
Ex. From the previous example, suppose that you receive triple the amount each day. On what day would you receive at least a million dollars?
6
A logarithmic equation is an equation with a logarithmic expression that contains a variable. You can solve logarithmic equations by using the properties of logarithms. Ex. Solve
a. b. 7
c. d.
8
Try These:
Ex. Solve.
a.
b. 9
Ex. Use a table and graph to solve.
a. b. 10
Try These:
Ex. Use a table and graph to solve.
a.
b.
c. 11