# Rewrite as single logarithm worksheet puzzle

You are welcome to copy the worksheets and lesson plans here for classroom use. Elementary Algebra is about manipulating mathematical expressions, with quantities represented by symbols e. Site Navigation Properties of Logarithms Logarithmic functions and exponential functions are connected to one another in that they are inverses of each other. You may recall that when two functions are inverses of each other, the x and y coordinates are swapped.

This leads to the most basic property involving logarithms which allows you to move back and forth between logarithmic and exponential forms of an expression. Change the exponential equation to logarithmic form. When changing between logarithmic and exponential forms, the base is always the same.

In the exponential form in this problem, the base is 2, so it will become the base in our logarithmic form.

## Practice Solutions

Because logarithms and exponents are inverses of each other, the x and y values change places. Since the base is the same whether we are dealing with an exponential or a logarithm, the base for this problem will be 5.

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We will exchange the 4 and the The was attached to the 5 and the 4 was by itself. In the logarithmic form, the will be by itself and the 4 will be attached to the 5.

So in exponential form is. This problem is nice because you can check it on your calculator to make sure your exponential equation is correct. In addition to the property that allows you to go back and forth between logarithms and exponents, there are other properties that allow you work with logarithmic expressions.

This property says that no matter what the base is, if you are taking the logarithm of 1, then the answer will always be 0. You can verify this by changing to an exponential form and getting. This property says that if the base and the number you are taking the logarithm of are the same, then your answer will always be 1.

This property allows you to take a logarithmic expression of two things that are multiplied, then you can separate those into two distinct expressions that are added together. You can also go the other way. Two log expressions that are added can be combined into a single log expression using multiplication.

This property allows you to take a logarithmic expression involving two things that are divided, then you can separate those into two distinct expressions that are subtracted. Two log expressions that are subtracted can be combined into a single log expression using division.

This property will be very useful in solving equations and application problems. It allows you to take the exponent in a logarithmic expression and bring it to the front as a coefficient. You can also go the other way and move a coefficient up so that it becomes an exponent.

So if properties 3, 4 and 5 can be used both ways, how do you know what should be done? That depends on the type of problem that is being asked. Use the properties of logs to write as a single logarithmic expression. Since this problem is asking us to combine log expressions into a single expression, we will be using the properties from right to left.

We usually begin these types of problems by taking any coefficients and writing them as exponents. Now there are two log terms that are added. We can combine those into a single log expression by multiplying the two parts together.

We have now condensed the original problem into a single logarithmic expression. Since we are trying to break the original expression up into separate pieces, we will be using our properties from left to right. We begin by taking the three things that are multiplied together and separating those into individual logarithms that are added together. There is an exponent in the middle term which can be brought down as a coefficient. This gives us There are no terms multiplied or divided nor are there any exponents in any of the terms.

We have expanded this expression as much as possible.Condense each expression to a single logarithm. 21) 2log 6 u − 8log 6 v 22) 8log 5 a + 2log 5 b 23) 8log 3 12 + 2log 3 5 24) 3log 4 u − 18 log 4 v 25) 2log 5 z + log 5 x 2 26) 6log uLSLrCV.Y V nAplHlo sroilgyhctgsz wrkeosBeLrevXe2d0.x C aMtaydoeK ewgiAtdhp 4ITnLfIiWnCijtQel rA6l1gQeGbVrJar 62p.U Worksheet by Kuta Software LLC Rewrite.

Sample Exponential and Logarithm Problems 1 Exponential Problems Example Solve 1 6 3x 2 = 36x+1. Solution: Note that Using the product and quotient properties of exponents we can rewrite the equation as ex+2 = e4 Example Write the expression log 6 30 log 6 10 as a single term.

Solution: This just means use the quotient rule: log. 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.

These tricky math puzzles are a fun way for 3rd and 4th graders to practice arithmetic and algebraic thinking. Click on a worksheet in the set below to see more info or download the PDF.