logarithmic functions integrated math 4 mrs. tyrpak

Logarithmic Functions

Integrated Math 4

Mrs. Tyrpak

What would the inverse of an exponential function look like?

Or how would we complete the following pattern?

Definition

Mathematicians had to define the inverse of an exponential function

described by “2 raised to what power gives us 6”

Evaluate each expression without a calculator

Converting between exponential and logarithmic Equations

1. Write as a logarithm.

2. Write as an exponential.

Solve each equation without a calculator

Other Logarithm Information

• Change of base formula:

Properties of Logarithms

–Product property

–Quotient property

–Power property

Inverse Properties of Logarithms

• Find and

Express the following logarithm as multiple logarithms

log𝑎3√ 𝑎2𝑏h6

Take 2 minutes to try this on your own…

log𝑐2√ 𝑎5h7

Express the following logarithms as a single logarithm

5 log𝑏𝑥− log𝑏 𝑦+14log𝑏(𝑧+2)

Take 2 minutes to try this on your own…

7 log𝑏𝑥+ log𝑏(𝑦+1)−12log𝑏 𝑧

Given that and , find the following…

Thanks for your attention!

Don’t forget to complete both the extension and enrichment assignments

before you move on.

Keep up the hard work!