Unit 7 – Logarithmic Function
Lesson 1 – Exploring the Logarithmic Function
Recall:
The Inverse of a Function
Determine the equation of the inverse
of 𝑦 = 𝑥 2 algebraically.
New:
Determine the inverse graphically
The Inverse of the Exponential Function 𝒚 = 𝒂𝒙
Determine the equation of the inverse
of 𝑦 = 2𝑥 algebraically.
Determine the inverse graphically
Exponential Form VS Logarithmic Form
The Logarithmic Function is the inverse of an exponential Function.
Exponential Form
𝑥 = 𝑎𝑦
Logarithmic Form
𝑦 = 𝑙𝑜𝑔𝑎 𝑥
Note:

These are equivalent expressions (just like 𝑦 = 𝑚𝑥 + 𝑏 y  mx  b and 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0).

𝑙𝑜𝑔𝑎 𝑥 means “the exponent that must be applied to the base a to get the value of x”
Graphs of Logarithmic Functions
Examples
1. Express 23 = 8 in Logarithmic Form.
2. Express 𝑙𝑜𝑔4 16 = 2 in Exponential Form.
1 𝑥
3. Sketch the inverse of the function𝑦 = (2) .