Transcript of "8.6 solving exponential and log equations"
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.
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