Question

calcule o valor de a: A= log8 27 . log25 16 . log81 6

Answer 1

log8 27= log2³ 3³= 3*1/3log2 3= 3log2 3

log25 16= log5² 4²=2*1/2log5 4=2log5 2²=
4log5 2

log81 6=log3⁴ 6= 1/4*log3 6= 1/4log3 3.2=1/4log3 3 + 1/4log3 2=1/4*1+1/4log3 2= 1/4+1/4log3 2

A=3log2 3 . 4log5 2 . 1/4(log3 2 + 1)
A=3 . 4 . 1/4 . log2 3 . log5 2 . (log3 2 +1)
A=3 . log2 3 . log5 2. (log3 2 +1)