if log3 5 = m and log 5 = t , find log4 3 in terms of t & m?

m = log3 5 = (log 5)/(log 3) => log 3 = t/m

4 = (10/5)^2 => log 4 = 2log (10/5) = 2(log 10 - log 5) = 2-2* (log 5) = 2-2t

=>

log4 3 = (log 3)/(log 4) = t/(m(2-2t))

You can use the laws of logarithms to get log4 3 in terms of log3 4, and then to get log3 4 in terms of log3 2.

You can also use log3 5 and log 5 to get log3 10. Then you can write log3 2 in terms of log3 10 and log3 5 and you have all the pieces you need.

log3 5 = log 5 / log 3

→ m = t / log 3

→ log 3 = t / m

Now,

log4 3 = log 3 / log 4

= t / (m log 4).

But Evgeniy has a better answer.

Just do your homework.But you can read the rules of logarithmic that your teacher should had give you at first.