# How To Solve Logarithmic Word Problems

Much of the power of logarithms is their usefulness in solving exponential equations.Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (p H balance, a measure of acidity and alkalinity).Let’s look at the Richter scale, a logarithmic function that is used to measure the magnitude of earthquakes.

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One extra point on the Richter scale can mean a lot more shaking!

With decibels, every increase of 10 means the sound is 10 times more intense.

Logarithmic and exponential functions can be used to model real-world situations.

Logarithmic functions are very helpful when working with phenomena that have a very wide range of values, because they allow you to keep the values you actually work with in a smaller range.

Visit Stack Exchange The question is The world population in 2000 was approximately 6.08 billion. The function that models this is \$\$ y = 6.08(10)^\$\$ where y represents the population in billions and t is the time in years after 2000.

Write and solve a logarithmic equation to determine what year the world population will exceed 7.5 billion.

Exponential functions are helpful with phenomena that change very quickly, or that grow or decay by a percentage over a particular time period.

We can think of logarithmic functions as the inverse of exponents.

To find the measurement of that size earthquake on the Richter scale, you find log 3920.

A calculator gives a value of 3.5932…or 3.6, when rounded to the nearest tenth.

## Comments How To Solve Logarithmic Word Problems

• ###### Solving Logarithmic Equations - ChiliMath

Solving Logarithmic Equations Generally, there are two types of logarithmic equations. Study each case carefully before you start looking at the worked examples below. Types of Logarithmic Equations The first type looks like this. If you have a single logarithm on each side of the equation having the same base then you can set the…

• ###### Logarithmic Functions solutions, examples, videos

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• ###### Algebra - Solving Logarithm Equations

In this section we will discuss a couple of methods for solving equations that contain logarithms. Also, as we’ll see, with one of the methods we will need to be careful of the results of the method as it is always possible that the method gives values that are, in fact, not solutions to the equation.…

• ###### Solving Logarithmic Equations Word Problems

Solving Logarithmic Equations Word Problems Example 1 INVESTMENT Mr. and Mrs. Mitchell are saving for their daughter’s college education. They invest \$10,000 in an account that pays 4.5% interest compounded continuously with the goal to have twice that amount in the account in ten years. a. Will the Mitchell’s reach their investment goal in ten years? Find the doubling time for the Mr.…

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• ###### Lesson OVERVIEW of lessons on logarithms, logarithmic.

OVERVIEW of lessons on logarithms, logarithmic equations and relevant word problems My lessons in this site on logarithms, logarithmic equations and relevant word problems are -…

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