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# C3 Help, logs watch

1. y = lnx

find in terms of y

i) log(2)X
ii) ln (x^2/e)
where(2) = to the base to

I'm so confused, what are the log rules/method for these type of questions
2. y = ln x = log(e) x

log(2) x = log(e) x / (log(e) 2) = lnx/ln2 = y/ln2

ln (x^2/e) = 2ln x - lne = 2y - 1

the three rules:
log ab = log a + log b
log a/b = log a - log b
log (a^b) = b*log a

also to change base,

log(a) b = [log(c) b]/[log(c) a]
3. cheers, it was the change of base rule 1 i never learnt.

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