Download Lesson 10-6 Solving Exponential Equations

Lesson 6-6 Solving Exponential Equations
Exponential equations are ___________________________________
__________________________________________________________.
Example 1:
Suppose 6x = 42
a) Estimate the value of x.
b) Solve the equation.
Step 1:
Estimate that x should be between _____ and ______.
Step 2:
Take the log of both sides.
Step 3:
Use the properties of logarithms to get the variable alone.
Example 2:
Solve 82x – 5 = 5x + 1
Change of Base Formula: ________________________________
_______________________________________________________.
Example 3:
Express each logarithm in terms of common logarithms.
Then approximate its value to three decimal places.
a) log8 77
b) log16 64
Growth and Decay
The general formula for growth and decay is ______________, where
______ is the final amount, _________ is the initial amount, _______ is
a constant, and _______ is the time.
Example 1:
Bacteria usually reproduce by a process known as
binary fission. In this type of reproduction, one bacterium divides,
forming two bacteria. Under ideal conditions, some bacteria can
reproduce every 20 minutes. Find the constant k for the growth of these
types of bacteria under ideal conditions and write the growth equation.
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Write down the formula to be used.
Fill in the information that is known.
Simplify the terms.
Take the ln of both sides.
Use your properties to simplify.
Solve for the missing value.
Example 2:
For a certain radioactive element, k is –0.377 when t is
measured in days. How long will it take 500 grams of the element to
reduce to 200 grams?
Example 3:
Radioactive iodine is used to determine the health of
the thyroid gland. It decays according to the equation y = ne-0.0856t,
where t is in days. Find the half-life of this substance.