1.Nilai dari ²Log3 + ²Log6 - 2Log9=2.³Log12+ ²Log24 - ³Log32=3.⁴Log3x - 4Log12x² + ⁴Log2x=4. ⁴Log 125=a maka 25 Log 8=5.³Log25 x ²Log9 x ⁵Log2/5
Answer (2)
Jawaban:1. 2log3 + 2log6 - 2log9= 2(log3 + log6 - log9)= 2log(3 × 6 / 9)= 2log(18 / 9)= 2log2= log(2^2)= log42. 3log12 + 2log24 - 3log32= log(12^3) + log(24^2) - log(32^3)= log(12^3 × 24^2 / 32^3)3. 4log(3x) - 4log(12x^2) + 4log(2x)= 4(log(3x) - log(12x^2) + log(2x))= 4log((3x × 2x) / (12x^2))= 4log(6x^2 / 12x^2)= 4log(1/2)= 4log2^(-1)= -4log24. Diketahui 4log125 = aKarena 125 = 5^3, maka4log125 = 4log5^3 = 12log5 = aJadi log5 = a/12Ditanya 25log8Karena 25 = 5^2 dan 8 = 2^3Maka 25log8 = log25^8 = log(5^2)^8 = log5^16 = 16log5 = 16 × a/12 = 4a/35. 3log25 × 2log9 × 5log(2/5)= log25^3 × log9^2 × log(2/5)^5= log15625 × log81 × log(32/3125)
Jawaban:Berikut adalah solusi detail untuk setiap soal: 1. ²Log3 + ²Log6 - ²Log9 =- Gunakan sifat logaritma: log A + log B = log (A * B) dan log A - log B = log (A / B)- ²Log (3 * 6 / 9) = ²Log (18/9) = ²Log 2- Karena ²Log 2 = 1- Jawaban: 12. ³Log12 + ²Log24 - ³Log32 =- Soal ini sepertinya ada kesalahan. Basis logaritma harus sama agar bisa disederhanakan langsung. Jika soalnya benar, maka tidak bisa disederhanakan lebih lanjut tanpa kalkulator.- Asumsi: Soal yang benar adalah ³Log12 + ³Log2 - ³Log32- Gunakan sifat logaritma: log A + log B = log (A * B) dan log A - log B = log (A / B)- ³Log (12 * 2 / 32) = ³Log (24/32) = ³Log (3/4)- Jawaban: ³Log (3/4)3. ⁴Log3x - ⁴Log12x² + ⁴Log2x =- Gunakan sifat logaritma: log A + log B = log (A * B) dan log A - log B = log (A / B)- ⁴Log ((3x * 2x) / (12x²)) = ⁴Log (6x² / 12x²) = ⁴Log (1/2)- ⁴Log (1/2) = ⁴Log (2^-1) = -1 * ⁴Log 2 = -1 * (1/2) = -1/2- Jawaban: -1/24. ⁴Log 125 = a maka 25Log 8 =- ⁴Log 125 = a -> (2²)Log (5³) = a -> (3/2) * ²Log 5 = a -> ²Log 5 = (2/3)a- 25Log 8 = (5²)Log (2³) = (3/2) * ⁵Log 2 = (3/2) * (1 / ²Log 5) = (3/2) * (1 / ((2/3)a)) = (3/2) * (3 / (2a)) = 9 / (4a)- Jawaban: 9 / (4a)@Ara14125. ³Log25 x ²Log9 x ⁵Log2/5 =- Gunakan sifat perubahan basis logaritma: log_a b = (log_c b) / (log_c a)- (³Log 25) * (²Log 9) * (⁵Log 2/5) = (³Log 5²) * (²Log 3²) * (⁵Log 2 - ⁵Log 5)- = 2(³Log 5) * 2(²Log 3) * (⁵Log 2 - 1)- = 4 * (³Log 5) * (²Log 3) * (⁵Log 2 - 1)- = 4 * (Log 5 / Log 3) * (Log 3 / Log 2) * (Log 2 / Log 5 - 1)- = 4 * (Log 5 / Log 2) * (Log 2 / Log 5 - 1)- = 4 * (1 - Log 5 / Log 2)- = 4 * (1 - ²Log 5)- Jawaban: 4(1 - ²Log 5)
