11 3 Exponential and Logarithmic Equations CHANGE OF

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11. 3 – Exponential and Logarithmic Equations

11. 3 – Exponential and Logarithmic Equations

CHANGE OF BASE FORMULA Ex: Rewrite log 515 using the change of base formula

CHANGE OF BASE FORMULA Ex: Rewrite log 515 using the change of base formula

Steps for solving exponential equations Take a common logarithm of each side ¡ Use

Steps for solving exponential equations Take a common logarithm of each side ¡ Use the power property of logarithms ¡ Solve for x by dividing ¡ Use a calculator to find the approximate value ¡

Review exponential equations ¡ 64 = 2

Review exponential equations ¡ 64 = 2

Solving Exponential Equations Solve . Round to the nearest ten-thousandth. 1. Take the log

Solving Exponential Equations Solve . Round to the nearest ten-thousandth. 1. Take the log of both sides 2. Use the power property 3. Solve for x. X=1. 2619 4. Use a calculator. Check your answer – 31. 2619=4

Another Example Solve . Round to the nearest ten-thousandth. 1. Take the log of

Another Example Solve . Round to the nearest ten-thousandth. 1. Take the log of both sides 2. Use the power property 3. Solve for x. X=4. 2009 – 4 = 0. 2009 4. Use a calculator. Check your answer – 30. 2009+4=101

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CHANGE OF BASE – HOW IT WORKS ¡ Use the change of base formula

CHANGE OF BASE – HOW IT WORKS ¡ Use the change of base formula to evaluate. Then convert it to a logarithm of base 2. 1. Rewrite using the change of base formula 2. Use a calculator 3. Write an equation to convert to base 2

CHANGE OF BASE – HOW IT WORKS 4. Substitute log 315=2. 4650 5. Rewrite

CHANGE OF BASE – HOW IT WORKS 4. Substitute log 315=2. 4650 5. Rewrite using the change of base formula 6. Multiply both sides of the equation by log 2 7. Use a calculator; simplify. 8. Write in exponential form. X=5. 5208 9. Use a calculator. Log 315 is approximately equal to 2. 4650 or log 25. 5208

Let’s try one ¡ Use the change of base formula to evaluate. Then convert

Let’s try one ¡ Use the change of base formula to evaluate. Then convert it to a logarithm of base 8. 1. Rewrite using the change of base formula 2. Use a calculator 3. Write an equation to convert to base 2

4. Substitute log 5400=3. 727 5. Rewrite using the change of base formula 6.

4. Substitute log 5400=3. 727 5. Rewrite using the change of base formula 6. Multiply both sides of the equation by log 8 7. Use a calculator; simplify. 8. Write in exponential form. X=2301 9. Use a calculator. Log 5400 is approximately equal to 3. 7227 or log 82301

SOLVING SIMPLE LOG EQUATIONS 1. Use the product property 2. Write in exponential form.

SOLVING SIMPLE LOG EQUATIONS 1. Use the product property 2. Write in exponential form. 3. Simplify 4. Solve for x.

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Solving exponential equations with a graphing calculator 1. Type two equations into y= 2.

Solving exponential equations with a graphing calculator 1. Type two equations into y= 2. Graph. Suggest Zoom fit (0) especially for large values 3. Use the calc function to find the intersection of the two graphs. Solution: 2. 0408

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