[PDF] [PDF] Converting Exponential Equations to Logarithmic Equations (Part 1)

[PDF] Changing from Logarithmic to Exponential Form

Changing from Logarithmic Form to Exponential Form In this example, the base of the logarithmic equation is 2 and as the base moved from the left side of the equation to the right side of the equation the number 5 moved up and became the exponent, creating an exponential equation

[PDF] Changing from Exponential to Logarithmic Form

Exponential equations can be written in logarithmic form and although the equations will look different, the equations still have the same meaning What is a  

[PDF] Examples of Changing From Logarithmic Form to Exponential Form

Example – Write the logarithmic equation 5 log z 67 = in exponential form In this example, the base 5 moved from the left side of the equal sign to the right side of  

[PDF] Examples of Changing From Exponential Form to Logarithmic Form

= 243 in logarithmic form In this example, the base is 3 and the base moved from the left side of the exponential equation to the right side 

[PDF] log logarithmic form: log exponential form: ln logarithmix form: ln

is the inverse of the natural exponential function The Natural Logarithmic function can be written in logarithmic form or exponential form Examine the comparison 

[PDF] Converting Exponential Equations to Logarithmic Equations (Part 1)

To solve each exponential equation, simply convert to logarithmic form Remember that a logarithm is an exponent, so set each exponent equal to the logarithm 

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23 août 2013 · Since 3 is the base and 4 is the exponent, we will have log base 3 of 81 equal to 4 2 The exponential form 4 1/2 = 2 is equivalent to the 

[PDF] 4 Exponential and logarithmic functions 41 Exponential Functions

, then u = v (This property is used when solving exponential equations that could be rewritten in the form a u = a

[PDF] Exponential and logarithm function

Question 1: How do you convert between the exponential and logarithmic forms of an equation? Exponential and logarithm functions are inverses of each other

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Name___________________________________ Date________________ Period____ Rewrite each equation in exponential form 1) log 11 121 = 2 2) log

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16-week Lesson 34 (8-week Lesson 28) Converting Exponential Equations to Logarithmic Equations (Part 1)

1 Once again the idea of using inverses to solve equations continues when solving exponential equations. The inverse of an exponential function is a logarithmic function, so we will convert exponential equations to logarithmic form to solve them. Example 1: Solve each of the following equations by converting to exponential form, and simplify your answers completely. To solve each exponential equation, simply convert to logarithmic form. Remember that a logarithm is an exponent, so set each exponent equal to the logarithm you set-up. converts to converts to converts to parentheses with the - in the denominator. The - in parentheses is part of a function (the argument of a logarithm), so adding, subtracting, multiplying, or dividing the logarithm will not affect the argument unless we use one of the Properties of Logarithms, such as the Power Rule:

All of these

expressions are correct ways to express the answer

Even though they

may look different, they are all equivalent.

16-week Lesson 34 (8-week Lesson 28) Converting Exponential Equations to Logarithmic Equations (Part 1)

2 Once again, keep in mind that exponential functions and logarithmic functions are inverses, which means each one undoes the other. Converting exponential equations to logarithmic equations gives us the primary way that we will use to solve exponential equations. There are other ways to solve exponential equations, such as using common logarithms and natural logarithms, but I will stick with simply converting to logarithmic form. Also, keep in mind that when converting from exponential form to logarithmic form, THE BASE DOES NOT CHANGE. Base ܽ form is base ܽ outputs because logarithms and exponentials are inverses. Example 2: Solve the exponential equation -ି௫ൌ͸ by converting to logarithmic form and then isolating the variable ݔ. LEAVE ANSWERS

IN EXACT FORM, DO NOT APPROXIMATE.

have been able to simplify as െ- or െ͵. Keep in mind that anytime a logarithm can be simplified, such as answer completely. Simplifying will also result in an easier answer to input in LON-

16-week Lesson 34 (8-week Lesson 28) Converting Exponential Equations to Logarithmic Equations (Part 1)

3 Example 3: Solve the exponential equation -௫ିଷൌͳ͸ by converting to logarithmic form and then isolating the variable ݔ. LEAVE ANSWERS

IN EXACT FORM, DO NOT APPROXIMATE.

Remember that a logarithm represents an exponent, so to simplify One benefit of solving exponential equations in this lesson as opposed to logarithmic equations like we solved in the previous lesson is that we are not required to check our answers. This is because exponential functions have unrestricted domains, so ݔ can represent any real number. Logarithmic functions have restricted domains, since the argument of a logarithm must be positive. Therefore when solving logarithmic equations, we must verify that our answers result in positive arguments. However when solving exponential equations, ݔ can be any real number, so checking our answers is not mandatory. In the case of Example 3, plugging ͹ back into the original equation for ݔ results in the following:

Again, checking

your answer on exponential equations is optional.

16-week Lesson 34 (8-week Lesson 28) Converting Exponential Equations to Logarithmic Equations (Part 1)

4 Example 4: Solve each exponential equation by converting to logarithmic form and then isolating the variable ݔ. LEAVE ANSWERS IN EXACT

FORM, DO NOT APPROXIMATE.

a. ͵ସି௫ൌͷ b. ͵௫మൌͳ- b.

16-week Lesson 34 (8-week Lesson 28) Converting Exponential Equations to Logarithmic Equations (Part 1)

5 c. ͵ହି௫ൌ-͹ d. ͵ d. A e. -ହ௫ାଷൌ͵ f. ଵ Once again, anytime a logarithm can be simplified, such as Ž‘‰ଷቀଵ above, it should be. Notice that because Ž‘‰ଷቀଵ ଼ଵቁ was able to be simplified, we ended up with an easier answer to input in LON-CAPA.

Answers to Examples:

4d. ݔൌଵ

ହ ; 4f. ݔൌquotesdbs_dbs7.pdfusesText_5