Solving Exponential Equations
 If two powers with the same base are
equal, then their exponents must be equal.
 To solve using this property:
 Rewrite equation so the bases match.
 Set exponents equal to each other.
 Solve for x.
Examples:
 Solve:
Your Turn!
 Solve
Solving by Taking Logs
 If it is not easy/possible to rewrite using
same bases, take the log (with base b) of
both sides.
 Examples:
Your Turn!
 Solve
More Examples: Taking Logs
 Not all equations will be that basic!
 Must get the exponential part by itself, first.
 Then, take the log of both sides.
 Last, continue solving for x.
 Example:
Example:
 Solve
Your Turn!
 Solve
Natural Base Exp. Equations
 Get the exponential part alone.
 Take the ln of each side.
 Example:
Exponential Models
 Newton’s Law of Cooling –
 the temperature T of a cooling substance is
modeled by
where:
t = time (in minutes)
T0 = initial temp. of substance
TR = room temp.
r = cooling rate
Example:
 Your mom is making soup for dinner. When
she takes it off the stove, it is 212ºF. The
room temp. is 70ºF and the cooling rate of the
soup is r = 0.046. How long will you have to
wait to eat the soup at a safe temp. of 100ºF?
Solving Log Equations
 For two logs with the same base:
 Example:
 Solve
Your Turn!
 Solve
Equations with One Log
 “Chop off the log” and write in exponential
form. Then solve for x.
 Example:
 Solve
Your Turn!
 Solve
Extraneous Solutions
 The domains of log functions are limited.
 This sometimes produces extraneous solutions.
 Always check answers in original equation.
 Example:
 Solve
Example:
 Solve
Your Turn!
 Solve