Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. Solving Logarithm Equations In this section we will now take a look at solving logarithmic equations, or equations with logarithms in them.

Properties 3 and 4 leads to a nice relationship between the logarithm and exponential function. This is a nice fact to remember on occasion.

We will be looking at this property in detail in a couple of sections. We will just need to be careful with these properties and make sure to use them correctly.

Also, note that there are no rules on how to break up the logarithm of the sum or difference of two terms. Note that all of the properties given to this point are valid for both the common and natural logarithms.

Example 4 Simplify each of the following logarithms. When we say simplify we really mean to say that we want to use as many of the logarithm properties as we can. In order to use Property 7 the whole term in the logarithm needs to be raised to the power.

We do, however, have a product inside the logarithm so we can use Property 5 on this logarithm. In these cases it is almost always best to deal with the quotient before dealing with the product.

Here is the first step in this part. Therefore, we need to have a set of parenthesis there to make sure that this is taken care of correctly.

The second logarithm is as simplified as we can make it. Also, we can only deal with exponents if the term as a whole is raised to the exponent. It needs to be the whole term squared, as in the first logarithm. Here is the final answer for this problem.

This next set of examples is probably more important than the previous set. We will be doing this kind of logarithm work in a couple of sections.

Example 5 Write each of the following as a single logarithm with a coefficient of 1. We will have expressions that look like the right side of the property and use the property to write it so it looks like the left side of the property.

This will use Property 7 in reverse. In this direction, Property 7 says that we can move the coefficient of a logarithm up to become a power on the term inside the logarithm.

Here is that step for this part. This means that we can use Property 5 in reverse.

Here is the answer for this part. When using Property 6 in reverse remember that the term from the logarithm that is subtracted off goes in the denominator of the quotient.

Here is the answer to this part. The reason for this will be apparent in the next step.U Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Properties of Logarithms Date_____ Period____ Expand each logarithm. 1) log (6 ⋅ 11) 2) log (5 ⋅ 3) 3) log (6 11) 5 4) log (3 ⋅ 23) 5) log 2 Condense each expression to a single logarithm.

13) log 3 − log 8 14) log 6 3. Condense each expression to a single logarithm. 21) 2log 6 u − 8log 6 v 22) 8log 5 a ewgiAtdhp 4ITnLfIiWnCijtQel rA6l1gQeGbVrJar 62p.U Worksheet by Kuta Software LLC Rewrite each equation in logarithmic form. tw5itQh1 LIAnhf0iDnBietMeI XAEligBeXbprnaB RWorksheet by Kuta Software LLC Answers to Logarithms: Expand, Condense.

Rewrite each equation in exponential form. Expand each logarithm. 7) log 9 x2 y6 8) log 5 (x ⋅ y ⋅ z4) Condense each expression to a single logarithm. 9) 6log 4 3 + log 4 8 2 6l1l q gr Pi6g AhDtRs6 1rTe Us1e9rXvXeAde.

v c 1M6a Fdoe D Xwei ztShl HImnWfPi Ln tixtFe V YA8l lg yetb6r2aN n2 alphabetnyc.comheet by Kuta Software LLC Answers to. Logarithm worksheets in this page cover the skills based on converting between logarithmic form and exponential form, evaluating logarithmic expressions, finding the value of the variable to make the equation correct, solving logarithmic equations, single logarithm, expanding logarithm using power rule, product rule and quotient rule, expressing the log value in algebraic expression.

Combining or Condensing Logarithms. Example 1: Combine or condense the following log expressions into a single logarithm: We have to rewrite 3 in logarithmic form such that it has a base of 4.

To construct it, use Rule 5 (Identity Rule) in reverse because it makes sense that 3 = log 4 (4 3). For this single logarithm worksheet, students use the quotient rule to rewrite given logarithms.

This two-page worksheet contains 5 multi-step problems. Answers are provided on the last page.

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Intro to Logarithms (article) | Khan Academy