Question

Prove
3log4=4log3
plz show the whole process

Answer 1

Here is the proof.
Let 3log4 = y  ... (1)

Taking logarithm on both the sides,

log 3log4 = log y

log 4 × log 3 = log y  [log am = m log a]

log 3 × log 4 = log y

log 4log 3 = log y  [m log a = log am]


Taking anti-logarithm on both the sides,

antilog (log 4log 3) = antilog (log y)

4log 3 = y  ... (2)

 

From (1) and (2), 3log4 = 4log 3


Hence, the result is proved.

Answer 2

Answer:

LHS

3log4=k(say)log3log4=logklog4log3=logk⋯(1)

RHS

4log3=l(say)log4log3=logllog3log4=logl⋯(2)

From (1)(2)

logk=logll=k3log4=4log3

Hence proved

Explanation:

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