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5.3.1 – Logarithmic Functions

5.3.1 – Logarithmic Functions. When given exponential functions, such as f(x) = a x , sometimes we needed to solve for x Doubling time Years to reach a particular amount Trouble is, we don’t have an exact way to solve for x. Log Function.

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5.3.1 – Logarithmic Functions

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  1. 5.3.1 – Logarithmic Functions

  2. When given exponential functions, such as f(x) = ax, sometimes we needed to solve for x • Doubling time • Years to reach a particular amount • Trouble is, we don’t have an exact way to solve for x

  3. Log Function • Luckily, we can use a logarithmic function to help us solve such problems • If a is a fixed positive number, and if x = ay, then; • y = logzx • a is the bsae of both functions/equations • OR, a to what power gives you x

  4. Properties • There are some simple properties we can use to help us better understand logs • Loga1 = 0 • Why? • Logaa = 1 • Why?

  5. Properties Cont’d • Loga(ax) = x (Knockdown Property) • aloga(x) = x • If no base is listed, we assume base 10

  6. Example. Evaluate the following logarithmic expressions: • a) log525 • b) log1/22 • c) log171

  7. Try these • D) log164 • E) log31 • F) log5(1/25) • G) 2log981

  8. Assignment • Pg. 411 • 13-23 odd

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