1. Exponential Equations
An exponential equation is an equation in which the variable appears in the exponent.
Guidelines for solving exponential equations
1. Isolate the exponential expression on one side of the equation.
2. Take the log of each side and “bring down the exponent.”
3. Solve for the variable.

2. Examples: Solve the following equations1. 2. 3. 4. 5.

3. Logarithmic Equations
A logarithmic equation is an equation in which the log of a variable appears in the equation.
Guidelines for solving exponential equations
1. Isolate the logarithmic term on one side of the equation; you may first need to combine logarithmic terms.
2. Write the equation in exponential form.
3. Solve for the variable.

4. Examples: Solve the following equations6. 7. 8. 9.

5. Ex 10: If I0 and I denote the intensity of light before
Ex 10: If I0 and I denote the intensity of light before and after going through a material and x is the distance (in feet) the light travels in the material, then according to the Beer-Lambert Law
where k is a constant depending on the type of material.
a. Solve for I.
b. For a certain lake, k = and the light intensity is I0 = 14 lumens. Find the light intensity at a depth of 20 feet.

6. Ex 11: A sum of $5000 is invested at an interest rate of. 9% per year
Ex 11: A sum of $5000 is invested at an interest rate of 9% per year. Find the time required for the money to double if the interest is compounded according to the following method.
a. Semiannual
b. Continuous

7. Ex 12: A sum of $1000 is invested at an interest rate of. 8% per year
Ex 12: A sum of $1000 is invested at an interest rate of 8% per year. Find the time required for the amount to grow to $4000 if interest is compounded continuously.
Ex 13: Find the annual percentage yield for an investment that earns interest at a rate of 6% per year, compounded daily.

8. Assignment (#31) S 5.4:
pg 424 – 425
#4-6,16,17,25,30,40-43,48,49,56-58,
70-72,75