8.5 – Exponential and Logarithmic Equations. CHANGE OF BASE FORMULA where M, b, and c are positive numbers and b, c do not equal one. Ex: Rewrite log.

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Presentation transcript:

8.5 – Exponential and Logarithmic Equations

CHANGE OF BASE FORMULA where M, b, and c are positive numbers and b, c do not equal one. Ex: Rewrite log 5 15 using the change of base formula

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

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

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

Let’s try some

CHANGE OF BASE – HOW IT WORKS  Use the change of base formula to evaluate. Then convert it to a logarithm of base 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 6. Multiply both sides of the equation by log2 7. Use a calculator; simplify. 8. Write in exponential form. 5. Rewrite using the change of base formula 4. Substitute log 3 15= X= Use a calculator. Log 3 15 is approximately equal to or log

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

6. Multiply both sides of the equation by log8 7. Use a calculator; simplify. 8. Write in exponential form. 5. Rewrite using the change of base formula 4. Substitute log 5 400=3.727 X= Use a calculator. Log is approximately equal to or log

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

Let’s try some

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