Question

Diketahui 4 log5 = m, 5 log7 = n. nyatakan bentuk berikut dalam m dan n.
a. 20 log28
b. 80 log35
c. 28 log100

Answer 1

4log5 = m
5log 7 = n
maka
4log7 =mn

a.
20log28=
4log28 / 4log20=
4log(4.7) / 4log(4.5)=
(4log4 + 4log7) / (4log + 4log5)=
(1+mn) / (1+m)

b.
80log35=
5log35 / 5log80=
5log(5.7) / 5log(4².5)=
(5log5 + 5log7) / (5log4² + 5log5)=
(1+n) / (2. 5log4 + 1)=
(1+n) / (2/4log5 + 1)=
(1+n) / (2/m + 1)=
(m+mn) / (2+m) atau m(n+1) / (2+m)

c.
28log100=
5log100 / 5log28=
5log(5².4) / 5log(4.7)=
(5log5² + 5log4) / (5log4 + 5log7)=
(2 + 1/4log5 ) / (1/4log5 + n) =
[(2m+1)/m] / [(mn+1)/m]=
(2m+1) / (mn+1)