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Solving Logarithmic Functions

Solving Logarithmic Functions. Math 3 Standard MM3A2. Steps: . Example 1:. 1) Isolate the Logarithm Condense the logarithm if you have to 2) Translate the equation from logarithmic form to exponential form. Steps: . Example 1:. 3) Solve for x

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Solving Logarithmic Functions

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  1. Solving Logarithmic Functions Math 3 Standard MM3A2

  2. Steps: Example 1: • 1) Isolate the Logarithm • Condense the logarithm if you have to • 2) Translate the equation from logarithmic form to exponential form

  3. Steps: Example 1: • 3) Solve for x • In this case, simplify the power first • Then, multiply by 3 • Take the square root of each side • When you take a square root, remember to use +

  4. Steps: Example 1: • 4) Check for extraneous solutions • Plug your solution(s) in to the original equation • Use your calculator to check it • This one gives a non-real answer • The only real solution is x=17.321

  5. Steps: Example 2: • 1) Isolate the Logarithm • Condense the logarithm if you have to • 2) Translate the equation from logarithmic form to exponential form

  6. Steps: Example 2: • 3) Solve for x • In this case, simplify the power first • Then, take the sixth root of each side • When you take a even root, remember to use +

  7. Steps: Example 2: • 4) Check for extraneous solutions • Plug your solution(s) in to the original equation • Use your calculator to check it • This one gives a non-real answer • The only real solution is x=6.813

  8. Steps: Example 3: • 1) Isolate the Logarithm • Condense the logarithm if you have to • 2) Translate the equation from logarithmic form to exponential form

  9. Steps: Example 3: • 3) Solve for x • In this case, simplify the power first • Then, divide by 5 • Then, take the third root of each side

  10. Steps: Example 3: • 4) Check for extraneous solutions • Plug your solution(s) in to the original equation • Use your calculator to check it • The solution is x=12.599

  11. Steps: Example 4: • 1) Isolate the Logarithm • You do not have to condense this one • 2) Translate the equation from logarithmic form to exponential form

  12. Steps: Example 4: • 3) Solve for x • In this case, simplify the power first • Then, add 13

  13. Steps: Example 4: • 4) Check for extraneous solutions • Plug your solution(s) in to the original equation • Use your calculator to check it • The solution is x=10013

  14. Steps: Example 5: • 1) Isolate the Logarithm • Condense the logarithm if you have to • 2) Translate the equation from logarithmic form to exponential form

  15. Steps: Example 5: • 3) Solve for x • In this case, simplify the power first • Then, multiply by 7

  16. Steps: Example 5: • 4) Check for extraneous solutions • Plug your solution(s) in to the original equation • Use your calculator to check it • The solution is x=1038.891

  17. Steps: Example 6: • 1) Isolate the Logarithm • You do not have to condense this logarithm • 2) Translate the equation from logarithmic form to exponential form

  18. Steps: Example 6: • 3) Solve for x • In this case, simplify the power first • Then, subtract 8 • Then, divide by 3

  19. Steps: Example 6: • 4) Check for extraneous solutions • Plug your solution(s) in to the original equation • Use your calculator to check it • The solution is x=1089669.791

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