Question

Jawab dengan caranya ;
1. Dik. nila a=9 , b=16 dan c=36.Nilai √(a^-1/3 b^-1/2 c)³ adalah...
2. Jika ³log5=p dan ^4log3=q maka ^12log60=...
3. ^5log√27.^9log125+^16log32=...
4. ^alog(1/b) . ^blog(1/c) . ^clog(1/a) =...

Answer 1

1) √(a^-1/3 b^-1/2 c)³  = (a^-1/3 b^-1/2 c)(^3/2)
= a^(-1/3 x 3/2). b^(-1/2x3/2). c^3/2
= a^(-1/2) . b^(-3/4). c^(3/2)
= 9^(-1/2) . 16^(-3/4) . 36^(3/2)
= 3^2(-1/2). 2^4(-3/4).6^2(3/2)
= 3^-1. 2^-3. 6^3
= 3^-1. 2^-3. 2^3. 3^3
= 3^(-1+3). 2^(-3+3)
= 3^2. 2^0
= 9(1) - 9
.
2)
12'log60 =  3'log 60 / 3'log 12
= 3'log (3x4x5)/(3'log 3x4)
= [ 3'log 3 + 3'log 4 + 3'log 5)/ (3'log 3 + 3'log 4)_
= [ 1+ 1/q + 1/p) / (1 + 1/q)
kalikan pq//pq
= [ pq ( 1 + 1/q + 1/p) / pq(1 + 1/q)
= (pq + p + q)/ (pq + p)
.
3)
(5^ 1/2)'log 3^3/2 . 3^2'log 5^3 + 2^4'log 2^5
= (3/2 : 1/2) 5'log 3 . (3/2). 3'log 5  + 5/4 . 2'log2
= 9/2 + 5/4 =  5 3/4 = 23/4
.
4)
= a'log b^-1. c'log c^-1. c'log a^-1
= (-1)(-1)(-1) ) a'log a
= -1