General Principles of Intellectual Property: Concepts of Intellectual Proper...
8.6 solving exponential and log equations
1.
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