# Logarithm Word Problems Worksheets

How to Tackle Logarithms in Word Problems Logarithmic word problems, in my experience, generally involve evaluating a given logarithmic equation at a given point and solving for a given variable; they're pretty straightforward. On the other hand, exponential word problems tend to be much more involved, requiring, among other things, that the student first generate the exponential equation, and perhaps then also find the value of one of the variables before beginning to answer the actual question. Since log problems are typically simpler, I'll start with them. Chemists define the acidity or alkalinity of a substance according to the formula. "pH = -log [H+]" where [H+] is the hydrogen ion concentration, measured in moles per litre. Solutions with a pH value of less than 7 are acidic; solutions with a pH value of greater than 7 are basic; solutions with a pH of 7 (such as pure water) are neutral. Suppose that you test apple juice and find that the hydrogen ion concentration is [H+] = 0.0003. Find the pH value and determine whether the juice is basic or acidic. You test some ammonia and determine the hydrogen ion concentration to be [H+] = 1.3 × 10-9. Find the pH value and determine whether the ammonia is basic or acidic. In each case, I need to evaluate the pH function at the given value of [H+]. a) In the case of the apple juice, the hydrogen ion concentration is [H+] = 0.0003, so: pH = -log[H+] = –log [0.0003] = 3.52287874528... ...which is less than 7, so this is acidic.

• ### Basic Lesson

Demonstrates general rules of simplifying logarithm word problems. Nancy invested \$6,200 in a three year CD that pays out five percent compounded annually. What is the total amount that will be in the account after three year?

• ### Intermediate Lesson

Explores how to use critical thinking skills when solving logarithm word problems. Billy borrowed \$45 from Zack eight months ago. Today, Billy paid Zack back \$102.50. What is the annual interest rate that Billy paid?

• ### Independent Practice 1

Example: John invested \$1254 in a six year CD that pays out five percent compounded annually. What is the amount that will be in the account after six year? The answers can be found below.

• ### Independent Practice 2

Example: Billy borrowed \$55 from Y six months ago. Today, Billy paid Y back \$7589. What is the annual interest rate that Billy paid?

• ### Homework Worksheet

Example problems are provided and explained. Like: Nancy has a savings bond that will be worth \$65,075.14 in eight years. The bond has an interest rate of 5% that is compounded every six months. What is the value of the bond?

• ### Topic Quiz

10 Logarithm Word problems. A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### What's Up With Word Problems?

To solve algebra word problems translate the problem into mathematical language using only the essential facts. A variable in an equation is just an unknown quantity; you can call it anything. Classify the problem into a familiar grouping of problems.