The Logarithm Decoder
Rewrite exponential equations as logarithms using the definition.
Equation
y = 3^x
Graph
Table
| x | y |
|---|---|
| 0 | 1 |
| 1 | 3 |
| 2 | 9 |
| 3 | 27 |
| 4 | 81 |
| 5 | 243 |
What this lesson covers
What you do
You shape the function y = b^x and watch the graph answer.
Challenges to clear
- Verify that 2^3 = 8. This means log₂(8) = 3.
- Verify that 2^2 = 4. This means log₂(4) = 2.
- Verify that 2^5 = 32. This means log₂(32) = 5.
- Powers of 5 this time — slide b to 5.
- There is a multiplier as well. Slide a until x = 2 reads 75: 5² = 25, so a is 3.
Check yourself
If 2^3 = 8, then log₂(8) = 3. Using the table for b=2, what is log₂(32)?
What does the logarithm log_b(y) represent in the equation y = b^x?
- 4 (because 32 / 8 = 4)
- 5 (because 2^5 = 32) — correct
- 6 (because 32 is large)
- 2 (because the base is 2)
- The base b
- The result y
- The exponent x — correct
- The sum of b and x
Think about it
- Set the base b to 2 and find the x where y = 8. That x IS log₂(8).