2. 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.
7. 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:
10. Natural Base Exp. Equations
Get the exponential part alone.
Take the ln of each side.
Example:
11. 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
12. 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?
17. Extraneous Solutions
The domains of log functions are limited.
This sometimes produces extraneous solutions.
Always check answers in original equation.
Example:
Solve