Jika deiketahui ² log 3 = a, dan ² log 5 = b, maka ² log 20/24 adalah?
A. 2(a+b)
B. b(a+1)
C. a/b
D. a-2b
E. 2+b/3+a
gunakan cara berserta penjelasanya
A. 2(a+b)
B. b(a+1)
C. a/b
D. a-2b
E. 2+b/3+a
gunakan cara berserta penjelasanya
Verified answer
JAWABAN
²log (20/24) = b - (a + 1)
PEMBAHASAN
²log 3 = a
²log 5 = b
²log (20/24)
= ²log (5/6)
= ²log 5 - ²log 6
= b - ²log (2 × 3)
= b - (²log 2 + ²log 3)
= b - (1 + a)
= b - (a + 1)
Jawab:
Penjelasan dengan langkah-langkah:
[tex]^2\log3 = a \ \text{dan} \ ^2\log5 = b[/tex]
[tex]^2\log(\frac{20}{24}) = \ ^2\log20 - \ ^2\log24[/tex]
[tex]= \ ^2\log(4\times5) - \ ^2\log(4\times 6)[/tex]
[tex]= \ ^2\log4+ \ ^2\log5 - ( \ ^2\log4 +\ ^2\log6)[/tex]
[tex]= \ ^2\log2^2 + \ ^2\log5 - ( \ 2\cdot^2\log2 + \ ^2\log(2\times 3))[/tex]
[tex]= 2 \cdot ^2\log2 + \ ^2\log5 -(\ 2\cdot^2\log2 + \ ^2\log2 + \ ^2\log3)[/tex]
[tex]= 2+b-(2+1+a)[/tex]
[tex]=b-a-1[/tex]