# LESSON 7-4 PROBLEM SOLVING PROPERTIES OF LOGARITHMS

Solve the linear equation as you normally would. The correct answer is 8. You can use either the common log or the natural log. Example 5b Evaluate log Example 5a Continued Evaluate log First notice that all of the logarithms have the same base. Rewrite this logarithmic equation as an exponential equation. Registration Forgot your password? Logarithmic equations may also involve inputs where the variable has a coefficient other than 1, or where the variable itself is squared. Because logarithms are exponents, you can derive the properties of logarithms from the properties of exponents. Use the power property of logarithms to simplify the logarithm on the left side of the equation. Simplify 2log2 8x log Example 1a Express as a single logarithm.

You can use either the common log or the natural log. When you have log b b mthe logarithm undoes the exponent, and the result is just m. Use a calculator to evaluate the leszon and the quotient. You can change a logarithm in one base to a logarithm in another base with the following formula.

Divide both sides by log 4 to get x by itself. No need to find 7 8. So, write a new equation that sets the exponents equal to each other. Look at these examples. Taking logarithms of both sides is helpful with exponential equations. The procedure is exactly the same. Lessn, you have two exponential expressions that are equal to each other. This is true with logarithms, too: When using the properties, it is absolutely necessary that the bases are the same.

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In this case, both sides have the same exponent, and this means the bases must be equal. Method 2 Change to base 4, because both 16 and 8 are powers of 2. The correct answer is 8. Part I Express each as a single logarithm. Check your answer by substituting the value of x into the original equation. This is also true for exponential and logarithmic equations.

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

You can use the properties of logarithms to combine these logarithms into one logarithm. Use the power property to rewrite. When the bases are the same, or the exponents are the same, you can just compare the parts that are different.

These are common logarithms, so the bases are all Changing the Base problwm a Logarithm Evaluate log Recognizing Inverses Simplify each expression.

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

Rewrite this logarithmic equation as an exponential equation. There are several strategies you can use to solve logarithmic equations. If the base were 10, using common logarithms would be better.

FRACTIONS NRICH PROBLEM SOLVING TASKS Method 2 Change to base 2, because both 32 and 8 are powers of 2. To use this website, you must agree to our Privacy Policyincluding cookie policy.

Rewrite this logarithm as an exponential equation. Method 1 Change to base Remember that logarithms and exponential functions are inverses.

You know x must be a little more than 2, because 17 is just a little more than Answer Use a calculator to evaluate the logarithms and the quotient. 