You use one of these two bases, as you can then use your calculator to find the values. The first is one you have used before: Round to the nearest hundredth. Example 2 Express log — log77 as a single logarithm. In this case, divide both sides by 3, then use the square root property to find the possible values for x. The equations may also include more than one logarithm. Part I Express each as a single logarithm.

In this case, both sides have the same exponent, and this means the bases must be equal. You could have used either the common log or the natural log with the example above. Example 5a Evaluate log Apply the change of base formula to switch from base 5 to base Method 2 Change to base 3, because both 27 and 9 are powers of 3. Simplify 2log2 8x log

When using the properties, it is absolutely necessary that the bases are the same. Example 5a Continued Evaluate log Write, evaluate, and graph logarithmic functions.

You can change a logarithm in one base to a logarithm in another base with the following formula. If the two expressions are equal, then their exponents must be equal. Answer Use a calculator to evaluate the logarithms and the quotient. Use the power property of logarithms to simplify the logarithm on the left.

Objectives Write equivalent forms for exponential and logarithmic functions.

Test the solution in the original equation. Look at these examples.

# Use the properties of logarithms (practice) | Khan Academy

There are several strategies you can use to solve logarithmic equations. You probably took the logarithms correctly and added 2 to both sides, but you forgot to divide by 3. The correct answer is 8.

The check shows that with rounding accounted for, a true statement results, so you know that the answer is correct. In this case, both sides have the same exponent, and this means the bases logqrithms be equal.

In these cases, you need to complete a few more steps in solving for the variable. Remember, when no base is written, that means the base is Use a calculator to evaluate the logarithms and the quotient.

When you have log b b mthe logarithm undoes the exponent, and the result is just m.

Example 5b Evaluate log Example 5a Evaluate log Example 1a Express as a single logarithm. Simplify 2log2 8x log Write a new equation that sets the bases equal to each other.

Example 3 Express as a product. No need to find 7 8. Use the power property of logarithms to simplify the logarithm on the left side of the equation.

## 7-4 Properties of Logarithms Warm Up Lesson Presentation Lesson Quiz

Part I Express each as a single logarithm. Recognizing Inverses Simplify each expression. Example 5 Continued Evaluate log Use the quotient property,to combine log 36 — pogarithms 3. These are common logarithms, so the bases are all The procedure is exactly the same. Take the common logarithm of both sides.

# Solving Exponential and Logarithmic Equations

Since the base is euse the natural logarithm. Here are two exponential expressions with the same base. The equations may also include more than one logarithm.