# Write as sum difference or multiple of logarithms properties

However, if we stick to the basics by carefully applying the rules of exponents in every step, we should have no problem conquering this problem! Rule 3: Power Rule The logarithm of an exponential number is the exponent times the logarithm of the base. The Quotient rule should deal with the fractional expressions by writing them as the difference of logs. The difference of the logs is the log of the quotient. Free Math Lessons, Videos, Quizzes and Worksheets Expanding Logarithms When you are asked to expand log expressions, your goal is to express a single logarithmic expression into many individual parts or components.

To find the log base a, where a is presumably some number other than 10 or e, otherwise you would just use the calculator, Take the log of the argument divided by the log of the base. Descriptions of Logarithm Rules The logarithm of the product of numbers is the sum of logarithms of individual numbers. Rule 7: Exponent of Log Rule Raising the logarithm of a number by its base equals the number. The log of a sum is NOT the sum of the logs.

### Express the following as a sum difference or multiple of logarithms

Common Mistakes I almost hesitate to put this section in here. Example 8: Expand the log expression The main power 3 can be placed out front as multiplier using the Power Rule. The log of a sum cannot be simplified. In this case, one of the exponents will be the log, and the other exponent will be the power you're raising the quantity to. The log of a sum is NOT the sum of the logs. Only when the argument is raised to a power can the exponent be turned into the coefficient. The base that you use doesn't matter, only that you use the same base for both the numerator and the denominator.

Common Mistakes I almost hesitate to put this section in here. That is, the numerator contains a variable with an exponent. The log of a sum cannot be simplified.

## Properties of logarithms examples

Only when the argument is raised to a power can the exponent be turned into the coefficient. Example 7: Expand the log expression I would immediately apply the Product Rule to separate the factors into a sum of logarithmic terms. What is to happen if you want to know the logarithm for some other base? Example 8: Expand the log expression The main power 3 can be placed out front as multiplier using the Power Rule. Well, remember that logarithms are exponents, and when you multiply, you're going to add the logarithms. Example 3: Expand the log expression Okay, so this one is also in fraction so Quotient Rule is the first step. In this case, one of the exponents will be the log, and the other exponent will be the power you're raising the quantity to.

The base that you use doesn't matter, only that you use the same base for both the numerator and the denominator.

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