Solve Exponential Equations
Match the bases to unlock the exponent.
Equation
y = 2^x
Graph
Table
| x | y |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
What this lesson covers
What you do
You shape the function y = b^x and watch the graph answer.
Challenges to clear
- Set the base b to 3. Look at the table to find the x value where y equals 27. This x is the solution to 3^x = 27.
- Same base: 3² = 9 — matching bases is what unlocks the exponent.
- This time the base is 4 — slide b there.
- There is a multiplier out front too. Slide a until x = 3 reads 128: 4³ is 64, so a must be 2.
Check yourself
If 5^y = 125, why can we say y = 3?
- Because 125 can be written as 5^3, and if the bases are the same, the exponents must match. — correct
- Because 125 divided by 5 is 25, and 25 is 5 squared, so we add 1 to get 3.
- Because the answer is always the number of digits in the result minus one.
- Because we divide the exponent 1 by the base 5 to get the answer.
Think about it
- 3^x = 27. How many threes multiply to 27?