PEAZIT Aha card
Go straight to resources ↓A logarithm finds the exponent
log_a(b) = c means a^c = b. A logarithm asks: to which power?
| Expression | Meaning |
|---|---|
| log_2(8) = ? | Find the exponent of 2 that produces 8. |
| 2^3 = 8 | Three factors of two give 8. |
| log_2(8) = 3 | The result is exponent 3, not base 2. |
One worked example
- log_2(8) = ?Find the exponent of 2 that produces 8.
- 2^3 = 8Three factors of two give 8.
- log_2(8) = 3The result is exponent 3, not base 2.
Watch out: For real logarithms, the argument b > 0 and the base a > 0, a ≠ 1. State the base explicitly.
Goal, prerequisites and card origin
What you will learn: Translate a logarithm into a question about a power.
What you need first: The base and exponent of a power.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
log_a(b) = c means a^c = b. A logarithm asks: to which power?