Dividing logarithms without using a calculator The problem I have is: (log16+log25-log36)/(log10-log3) (log is base 10 here)

Jonas Huff

Jonas Huff

Answered question

2022-11-11

Dividing logarithms without using a calculator
The problem I have is: log 16 + log 25 log 36 log 10 log 3
(log is base 10 here)
I have the answer as 2 but no idea how to reach it..
I need to work this out without the use of a calculator but I can't get my head round it. I know that
log ( 16 ) = log ( 4 2 ) = 2 ( log 4 ) log 25 = 2 ( log 5 )
I can add \logs together when they all are a power of the same number e.g.
log ( 64 ) + log ( 32 ) = log ( 2 6 ) + log ( 2 5 ) = 6 ( log 2 ) + 5 ( log 2 ) = 11 ( log 2 )
I might just be over thinking it or over complicating it but I'd really appreciate some help here. Thanks.

Answer & Explanation

Kayleigh Cross

Kayleigh Cross

Beginner2022-11-12Added 19 answers

log 16 + log 25 log 36 = log ( 16 25 36 ) = log ( ( 4 5 6 ) 2 ) = 2 log ( 20 6 ) = 2 log ( 10 3 )
log 10 log 3 = log ( 10 3 )
2 log ( 10 3 ) log ( 10 3 ) = 2
charmbraqdy

charmbraqdy

Beginner2022-11-13Added 4 answers

Hint: Use log a + log b = log a b and log a log b = log a b

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?