using properties to combine and condense logarithms

Step 2: Apply Property 3 or 4 to change the addition or subtraction of the logarithms to multiplication or division. You will get the same answer that equals 2 by using the property that log b b x = x. Step for Condensing Logarithms: Step 1: Apply Property 5 and move the number in front of the logarithm to the exponent of the variable. 2(In(Ve ) In(xy)) - Answer Keypa Keyboard Short If you wish to enter log or In, you must use the keypad. Transcribed image text: Condense the expression to a single logarithm with a leading coefficient of 1 using the properties of logarithms. Often, using the rules in the order quotient. Transcribed Image Text: Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1. We can also apply the logarithm rules backwards to combine logarithms. Remember, so means and y must be 2, which means. To expand logarithms, write them as a sum or difference of logarithms where the power rule is applied if necessary. Using that property and the Laws of Exponents we get these useful properties. This makes sense when you convert the statement to the equivalent exponential equation. One important but basic property of logarithms is log b b x = x. As a quick refresher, here are the exponent properties. Since logarithms are so closely related to exponential expressions, it is not surprising that the properties of logarithms are very similar to the properties of exponents. There are a number of properties that will help you simplify complex logarithmic expressions. This is how we will be using the Properties of Logarithms in this class, to combine logarithms in order to reduce the number logarithms we have to just one, so that we can then convert that one logarithm to exponential form to solve. These properties help you take a complicated expression or equation and simplify it. In Example 1, the Properties of Logarithms were only used to combine logarithms in each problem.

Throughout your study of algebra, you have come across many properties-such as the commutative, associative, and distributive properties.

Using properties to combine and condense logarithms