Equation in Logarithm We have (log_45)=a (log_56)= b and we have to find (log_32)

Cristofer Watson

Cristofer Watson

Answered question

2022-10-30

Equation in Logarithm
We have
log 4 5 = a
log 5 6 = b
and we have to find log 3 2
I tried the question but because of the different bases I was not able to get the solution.

Answer & Explanation

RamPatWeese2w

RamPatWeese2w

Beginner2022-10-31Added 15 answers

Please verify my answer. I used : log a ( b ) = log ( a ) log ( b ) this formula and got
log 5 6 = b
= log 5 3 + log 5 2 = log ( 3 ) log ( 5 ) + log ( 2 ) log ( 5 ) = b
log 3 + log 2 = b log 5 this is our equation 1
Then we have log 4 5 = a
= log ( 5 ) log ( 4 ) = a
= log ( 5 ) 2 log ( 2 ) = a
= log 5 = 2 log 2 a this end with second equationa after solving the equation i got
log ( 3 ) log ( 2 = 2 a b 1
log 3 2 = 1 2 a b 1
varsa1m

varsa1m

Beginner2022-11-01Added 4 answers

I will use a different approach, and will end up with the same solution that you have reached, thus verifying you answer.
We are given log 4 5 = a and log 5 6 = b, and wish to find log 3 2
So, 4 a = 5, 5 b = 6, 3 c = 2, and the objective is to find c in terms of a and b
Thus 5 b = ( 4 a ) b = 4 a b = 6 = 3 2
4 a b = 2 2 a b = 3 2
leading to
3 = 2 2 a b 1
Raising both sides to the power 1 ( 2 a b 1 ) , we end up with
3 1 2 a b 1 = 2
Resulting in
c = 1 2 a b 1

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