prove that 27^log2=8^log3

Question

Hint : Take log both the sides

Answer 1

27^log2=8^log3   take log of both sides: log(27^log2)=log(8^log3)

bring down the exponent so  (log2)log27=(log3)log8  

then log27/log3=log8/log2 

 

use identity  log_ax/log_ab=log_bx     so that

log₃27=log₂8  --> 3=3   (which is true)