PEAZIT Aha card
Go straight to resources ↓Logarithmic equations: check the input first
A logarithm needs a positive argument. Then rewrite the equation as a power.
| Expression | Meaning |
|---|---|
| log_2(x − 1) = 3; x > 1 | The domain requires x − 1 > 0. |
| x − 1 = 2^3 = 8 | Use the definition of a logarithm. |
| x = 9 | The value 9 satisfies x > 1. |
One worked example
- log_2(x − 1) = 3; x > 1The domain requires x − 1 > 0.
- x − 1 = 2^3 = 8Use the definition of a logarithm.
- x = 9The value 9 satisfies x > 1.
Watch out: Check the original arguments after transformations. log(a + b) does not equal log(a) + log(b).
Goal, prerequisites and card origin
What you will learn: Solve a simple logarithmic equation and check its domain.
What you need first: The meaning of logarithms and linear equations.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
A logarithm needs a positive argument. Then rewrite the equation as a power.