Jawabanmu

2014-09-02T22:04:37+07:00
A. 6log75 = log75/log6
karena 2 log 3 = a, maka log 3=a log2
karena 3 log 5 = b, maka log 5=b log3

Maka log75 = log(5x5x3),
log5+log5+log3 = b log3 + b log3 + log3
= 2b log3+log3
= 2b (a log2) + a log2

Dan log6 = log(2x3)
log2+log3 = log2+a log2

Maka 6log 75 = (2b (a log2) + a log 2) / log 2 + a log 2
                         = log 2 (2ba + a) / log 2 (1+a)
                         = (2ba + a)/(1+a)

B. 9log120 = log120/log9
karena 2 log 3 = a, maka log 3=a log2
karena 3 log 5 = b, maka log 5=b log3

Maka log120 = log(5x5x3x2x2),
log5+log5+log3+log2+log2 = b log3 + b log3 + log3 + (log3)/a +(log3)/a
= 2b log3 + log3 + 2log3)/a
= log3(2b+1+2/a)

Dan log9 = log(3x3)
= log3+log3
= 2 log3

Maka 9log 120 =
log3(2b+1+2/a) / 2 log3
                        =
(2b+1+2/a) / 2
                       






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