5.3.1 – Logarithmic Functions

• 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

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

Properties

• There are some simple properties we can use to help us better understand logs

• Loga1 = 0– Why?

• Logaa = 1– Why?

Properties Cont’d

• Loga(ax) = x (Knockdown Property)

• aloga(x) = x

• If no base is listed, we assume base 10

• Example. Evaluate the following logarithmic expressions:

• a) log525

• b) log1/22

• c) log171

Try these

• D) log164

• E) log31

• F) log5(1/25)

• G) 2log981

• Assignment• Pg. 411• 13-23 odd