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4 -4 Day 1: Logarithmic Functions

4 -4 Day 1: Logarithmic Functions. Everything in Life Has an Opposite. What would the opposite operation of be?. If we were to try to solve the equation below, what steps would we take to get x by itself?. Would Square Rooting Both sides get x by itself??.

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4 -4 Day 1: Logarithmic Functions

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  1. 4-4 Day 1: Logarithmic Functions

  2. Everything in Life Has an Opposite

  3. What would the opposite operation of be? If we were to try to solve the equation below, what steps would we take to get x by itself? Would Square Rooting Both sides get x by itself?? Would Squaring Both sides get x by itself??

  4. John Napier created a Operation to Solve this Delemma… Logarithms are considered the Opposite Operation of exponential functions, like Def: Let b and y be positive numbers, b≠0. The logarithm of y with base b is denoted by: If and only if

  5. Let’s Take a Closer Look… Ex 1: Simplify the expression Plug the command log (100) in the calculator. If there is no base specified, the base is 10 (Called a common logarithm.

  6. Let’s Put it all together… Ex2: Rewrite the logarithm in exponential form. 2 a. b. 7 = 49 Just remember to make a circle! x = 64 4

  7. Ex 2c: Rewrite the exponent as a logarithm.

  8. Ex 3: Evaluate the expression without using a calculator: This means we’re asking ourselves 3 to what power gives us 9?? a. b. c. = x x = 2 = x x = -3 = x x = 9

  9. Ex 4: Use a calculator to evaluate the expression: a. b. = 1.903 Note: If the base is not specified, you’re in base 10. = 1.022 Note: Ln called the “Natural Logarithm,” is in base e.

  10. Ex 5: Simplify the Expression Because the logarithm and the exponent have the same base, they cancel each other out… a. b. c. = k = 2 = 6x

  11. Exit Slip: 1). Evaluate the Expression without using a calculator: 2). Simplify the Expression:

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