Logarithm | Common Mistake

A common mistake occurs normally during simplification to a single logarithm term.

Question like,

" Simplify log X - log Y + log Z into a single term "

catches many students who are careless.

What is the error or mistake made?
- Doing the solving at one go when not familiar with the logarithmic rules
- Sign interpretation

Wrong answer given: log X/(YZ)

Correct answer: log XZ/Y

"log Z" is commonly taken to follow the previous log term, which is, "- log Y ".
Since "- log Y " causes the "Y" to be a denominator, "Z" is also taken to be a denominator too!

This is a mis-cue. A mental slip, mathematically.

Advise:
Look at the sign carefully before jumping to conclusion.
Go slow in the combination to a single log term.

Remember the idiom: "Slow and steady wins the race"

You can apply this to log simplification when you are new to it.

Cheers! :-D

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