Explain logarithms with a simple example
The short version: logarithms refers to the inverse of exponentiation, answering the question "what power gives this number?". A quick example makes it concrete — log₂ 8 = 3 because 2³ = 8.
How to approach it step by step
Once one example makes sense, the method generalises: use log(ab) = log a + log b, log(a/b) = log a − log b and log(aⁿ) = n log a to simplify first. In a visual interactive session the example is built on screen piece by piece, so you see which quantity changes at each step instead of only reading a final answer. Ask for a harder variant and the explanation adapts on the spot.
Worked example
log₂ 8 = 3 because 2³ = 8.
The mistake most learners make
Assuming log(a + b) can be split into log a + log b, which is not valid.
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