Worked example 1
Find x if log₅ x = 3.
Remember: Rewrite the logarithm as an index: logₐ N = k means aᵏ = N.
- logₐ N = k means aᵏ = N, so x = 5³.
- So x = 125.
Use the definition of a logarithm to find an unknown
Follow this one with me, a step at a time. Try to guess each step first.
Common mistakes
- The index is one out. Count the factors of the base again.
- Multiplied the base by the index. logₐ x = k means aᵏ = x, a repeated multiplication.
- Added the base and the index.
One at a time. A wrong answer gets a second try, so have a go.
Question 1
Find x if log₆ x = 5.
Question 2
Find x if log₇ x = −3.
Question 3
Find x if log₆ x = 2.
Topic quiz
Five questions on this topic, marked at the end. No hints and no answers along the way — that is what makes the result mean something.
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