inverse operations

1. Lesson 2.3
Inverting Operations

2. Introduction To Logarithms
Logarithms were originally
developed to simplify complex
arithmetic calculations.
They were designed to transform
multiplicative processes
into additive ones.

3. Desmos Activity
Instructions:
→Go to 👉 https://www.desmos.com/calculator
→ Enter each of the the following equations to produce their graphs.
1. y = 2x
2. x = 2y (Inverse of 1)
3. log2 x = y
What do you notice?

4. What is a logarithm ?
Logarithm is the inverse of exponential
function for
x>0 and b>0 , b≠1,
y = Logb x is equivalent to by = x
The function f(x) = Logb x is the logarithmic function with base ‘b’

5. Forms
Logarithmic form:
y = Logb x
Exponential form:
by = x

6. Notice
Logarithmic form: Where is the exponent and base.
y = Logb x
Exponential form:
by = x
Base of the logarithm is the base of the exponent.

7. Example 1: Exponential to Log
Write 23 = 8 in logarithmic form

8. Example 2: Exponential to Log
Write 42 = 16 in logarithmic form

9. Example 3: Exponential to Log
Write 2-3 = 1/8 in logarithmic form

10. Practice
Write 72 = 49 in logarithmic form

11. Practice
Write 50 = 1 in logarithmic form

12. Practice
Write 10-2 = 1/100 in logarithmic form

13. Practice
Write 161/2 = 4 in logarithmic form

14. Example 1: Log to Exponential
Write Log3 81 = 4 in logarithmic form

15. Example 2: Log to Exponential
Write Log2 1/8 = -3 in logarithmic form

16. Practice
Write Log10 100 = 2 in logarithmic form

17. Practice
Write Log5 1/125 = -3 in logarithmic form

18. Practice
Write Log27 3 = 1/3 in logarithmic form