1. Solving Equations with Logs

2. Exponential and Log Equations

3. Hit it with a log!

4. Let’s try another

5. Another example First, isolate the exponential term by dividing by 5 Now what? Hit it with a log! Use properties of logs to kick the exponent out front. Divide by log3 Subtract 4

6. Carbon Dating Carbon dating is a process used to measure the age of fossils and other remnants of once-living things. This is done my measuring the remaining amount of the radioactive element Carbon-14. C- 14 decays exponentially and has a half life of 5730 years. The formula for determining how much carbon is left after t years is C(t) = C 0 e − 0.0001216 t. If a newly found fossil has 12% of the original amount of C-14, how old is the fossil?

7. Your turn!

8. When do I use each method? By now, you may be a little overwhelmed with all of our methods for solving exponentials and logs, so let’s break it down to determine when to use each method. 1. If your equation is in log form, convert to exponential form (the loop). If it’s already in exponential form, leave it. 2. Once in exponential form, if your variable is the base, just take the given root of both sides to solve. 3. If the variable is in the exponent, try to rewrite both sides of the equation with the same base, then set the exponents equal and solve. 4. If you cannot rewrite with the same base, hit both sides with a log to bring your variable out front, then solve for the variable.

9. Examples: Choose the method needed and solve each for x.