M212 Algebra II Section 6.5 – 6.7 Review Sheet
Section 6.5 Applications of Common Logarithms
1) Using the common log (log10) to solve problems like 4x = 17.
2) Using the Change-of-Base Formula.
Section 6.6 The Natural Base, e
1) Using your calculator to evaluate ex and ln(x) expressions.
2) Rewriting natural exponent functions (ex = 4) as natural log functions (ln(4) = x) and vice versa.
3) Using the natural log to solve problems like 4x = 17
4) Using the Continuous Compounding Formula (A = Pert).
5) Figuring out how long it takes to double, triple, quadruple, etc. an initial investment.
Section 6.7 Solving Equations and Applications
1) Knowing the techniques for solving various types of problems containing logs and exponents
a. If the variable you are solving for is inside a log expression, isolate the log expression and then
convert it to an exponential expression. This will get the variable by itself.
b. If the variable you are solving for is inside an exponential expression, isolate the exponential
expression and then convert it to a log expression. This will get the variable by itself.
c. If you have logs everywhere in the expression, get a single log expression on both sides of the
equal sign and then the insides of the logs will be the same (just make sure your final answer
doesn’t cause you to take the log of a negative number in the original equation).
d. If you have exponential expressions everywhere in the expression, get a single exponential
expression on both sides of the equal sign (both exponential expressions must have the same
base) and then the insides of the exponents will be the same.
e. Don’t forget the “Change of Base” formula. It is helpful to solve some problems.
2) Solving problems like the application problems covered.
a. Plug in what you know from the problem and then figure out what you need to do to solve it. It
is often like part 1 above.
M212 Algebra II Section 6.5 – 6.7 Review Sheet
Additional Practice Problems
M212 Algebra II Section 6.5 – 6.7 Review Sheet
Additional Word Problems
1. $1,000 is invested at 6.5% compounded continuously.
a. How much is in the account after 1 year
b. How long will it take for the initial estimate to triple in value?
2. Bones found in an ancient cave contain 62% of their original amount of carbon-14. Use the
equation N t   N 0 e 0.00012t to estimate the age of the bones.
3.
Cooling Time of a Pizza: A pizza baked at 450 degrees Fahrenheit is removed from the oven
into a room that is a constant 70 degrees Fahrenheit. After 5 minutes, the pizza is at 300 degrees
Fahrenheit.
a) Write an equation for the temperature of the pizza as a function of time in minutes.
b) What temperature is the pizza after 30 minutes?
M212 Algebra II Section 6.5 – 6.7 Review Sheet
Additional Practice Problem Answers
M212 Algebra II Section 6.5 – 6.7 Review Sheet