I'm in doubt on simplifying the expression:

Deja Vaughn

Deja Vaughn

Answered question

2022-04-08

I'm in doubt on simplifying the expression: log26log49
Working on it I've got: log26log292
There's anyway to simplify it more ? I'm learning logarithms now so I'm not aware of all properties and tricks.
Thanks in advance

Answer & Explanation

cadhail6n1t

cadhail6n1t

Beginner2022-04-09Added 14 answers

You can do a bit more simplification. The important properties of the log function are, for any base a>0,
loga(bc)=logab+logac, so, for example, log26=log22+log23
loga(bc)=logablogac
logabn=nlogab
logab=1logba
(logab)(logbc)=logac
logaa=1
So, for example, we can simplify log26log49 as
log26log49=log2(23)log4(32)
=log22+log232log43        using the first and third identities
=1+log232log43          using the sixth identity
=1+log232log42log23          using the fifth
=1+log232log23log24          using the fourth
=1+log232log232          using the third
=1+log23log23          using a bit of algebra
=1

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