Question

Diketahui 2log3=a 3log5=b nyatakan logaritma berikut dalam a dan b

1. 2log15
2. 4log75
3. 25log36
4. 2log5
5. 30log150
6. 100log50

mohon bantuannya

Answer 1

Ketikkan jawabanmu di sini

Answer 2

^2log3=a    => log3/log2=a
^3log5=b    => log5/log3=b
1. ^2log 15= ^2log(3x5)= ^2log3+^2log5
               = a+b.^2log3= a+b.a=a+ab
2. ^4log 75= log 75/log 4=log(5^2x3)/ log 4
               = (^3log 5^2 + ^3log 3)/^3log4=(2(b) +1)/2(^3log3/a)
               =(2b+1)/2x1/a= (2b+1)/2/a= (2b+1)Xa/2= (2ab+a)/2
3. ^25log 36= ^2log36/^2log25= (^2log(3^2x2^2))/^2log 5
                 = (^2log 3^2+^2log 2^2)/log 5^2
                 = (2 ^2log3+ 2 ^2log2)/ 2 ^2log5
                 = (2a+ 2(^2log3/a))/2(^2log3.b)
                 = (2a+2.1)/2ab= (2a+2)/2ab= 2(a+1)/2.ab=(a+1)/ab
4. ^2log5 = ^2 log 3.b= ab
5. ^30log 150= ^2log150/^2log30
                   =(^2log(2.3.5^2))/(^2log(2.3.5))
                   =(^2log2+^2log3+2^2log5)/(^2log2+^2log3+^2log5)
                   =(1+a+2(b.^2log3))/(1+a+b.log3)
                   =(1+a+2(b.a))/(1+a+b.a)= (1+a+2ab)/(1+a+ab)