Showing posts with label logarithm. Show all posts
Showing posts with label logarithm. Show all posts

Saturday, May 4, 2013

Intermediate Algebra Exam #4

Click on the 10 question exam covering topics in chapter 7. Give yourself one hour to try all of the problems and then come back and check your answers.

IA Sample Exam #4 ]
8. A $1,000 investment is made at an annual interest rate of  7 3/4% that is compounded quarterly.  How long will it take the investment to double?
9. Francium-223 has a half-life of about 22 minutes. How much of a 3-microgram sample of francium-223 will be left after 5 minutes of decay? Round off answer to the nearest hundredth of a microgram.
10. In the year 2000 a certain small town had a population of 72,000 people.  In the year 2010 the population was estimated to have grown to 108,000 people. If the population continues to grow exponentially at this rate, estimate the population in the year 2016.

Monday, November 19, 2012

Solving Logarithmic Equations

Use the one-to-one property for logarithms to solve logarithmic equations. If we are given an equation with a logarithm of the same base on both sides we may simply equate the arguments.

   Step 1: Use the rules of exponents to isolate a logarithmic expression (with the same base) on both sides of the equation.
   Step 2: Set the arguments equal to each other.
   Step 3: Solve the resulting equation.
   Step 4: Check your answers.
Be sure to check to see if the solutions that you obtain solve the original logarithmic equation. In this study guide we will put a check mark next to the solution after we determine that it really does solve the equation. This process sometimes results in extraneous solutions so we must check our answers.

Of course, equations like these are very special.  Most of the problems that we will encounter will not have a logarithm on both sides. The steps for solving them follow.

   Step 1: Use the properties of the logarithm to isolate the log on one side.
   Step 2: Apply the definition of the logarithm and rewrite it as an exponential equation.
   Step 3: Solve the resulting equation.
   Step 4: Check your answers.
If the answer to the logarithmic equation makes the argument negative then it is extraneous.  This does not preclude negative answers. We must be sure to check all of our solutions.

Instructional Video: Solving Logarithmic Equations

Tip:  Not all negative solutions are extraneous!  Look at the previous set of problems and see that some have negative answers. The check mark indicates that we actually plugged the answers in to see that they do indeed solve the original.  Please do not skip this step, extraneous solutions occur often.
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