Berikut merupakan jawaban dari operasi perhitungan logaritma di atas:
2. c. [tex]^3log7[/tex] x [tex]^{25}log32[/tex] x [tex]^{49}log81[/tex] = [tex]^5log32[/tex]
d. [tex]^2log1/243[/tex] x [tex]^5log1/125[/tex] x [tex]^3log1/16[/tex] = -60
3. Jika diketahui [tex]^2log3 = m[/tex] dan [tex]^3log5 = n[/tex], maka:
- [tex]^8log18 = m[/tex]
- [tex]^{12}log25[/tex] = [tex]\frac{2n}{ ^3log4 + 1}[/tex]
- [tex]^{18}log75[/tex] = [tex]\frac{1 + 2n }{2 +^3log2}[/tex]
Penjelasan dengan langkah-langkah
2. c. Diketahui: [tex]^3log7[/tex] x [tex]^{25}log32[/tex] x [tex]^{49}log81[/tex]
Ditanya: Hasil perkalian logaritma?
Jawab:
[tex]^3log7[/tex] x [tex]^{25}log32[/tex] x [tex]^{49}log81[/tex]
= [tex]^3log7[/tex] x [tex]^{25}log32[/tex] x [tex]^{49}log81[/tex]
= [tex]^3log7[/tex] x [tex]^{7^2}log3^4[/tex] x [tex]^{5^2}log2^5[/tex]
= (4 x ½ [tex]^7log3[/tex]) x [tex]^3log7[/tex] x (5 x ½ [tex]^5log 2[/tex])
= 2 x ([tex]^7log3[/tex] x [tex]^3log7[/tex]) x 5/2 x [tex]^5log2[/tex]
= 2 x 5/2 x 1 x [tex]^5log2[/tex]
= 5 x [tex]^5log2[/tex]
= [tex]^5log2^5[/tex]
= [tex]^5log32[/tex]
d. Diketahui: ^2log1/243 x ^5log1/125 x ^3log1/16
Ditanya: Hasil perkalian logaritma?
Jawab:
[tex]^2log1/243[/tex] x [tex]^5log1/125[/tex] x [tex]^3log1/16[/tex]
= [tex]^2log1/3^5[/tex] x [tex]^5log1/5^3[/tex] x [tex]^3log1/2^4[/tex]
= (-5) x [tex]^2log3[/tex] x (-3) x [tex]^5log5[/tex] x (-4) x [tex]^3log2[/tex]
= (-5)(-3)(-4) x ([tex]^2log3[/tex] x [tex]^3log2[/tex]) x [tex]^5log5[/tex]
= -60 x 1 x 1
= -60
3. Diketahui:
- [tex]^2log3 = m[/tex]
- [tex]^3log5 = n[/tex]
Ditanya:
Nyatakan dalam m dan n:
- [tex]^8log18[/tex]
- [tex]^{12}log25[/tex]
- [tex]^{18}log75[/tex]
Jawab:
[tex]^8log18[/tex]
= [tex]^8log2 + ^8log9[/tex]
= [tex]^2(^3)log2 + ^2(^3)log3^2[/tex]
= 1/3 x [tex]^2log2[/tex] + 2/3 x [tex]^2log3[/tex]
= 1/3 x 1 + 2/3 x m
= 3/3 x m
= m
[tex]^{12}log25[/tex]
= [tex]^3log25 : ^3log12[/tex]
= [tex]^3log5^2 : ^3log(4)(3)[/tex]
= 2 x [tex]^3log5 : ^3log4 + ^3log3[/tex]
= 2 x n : [tex]^3log4[/tex] + 1
= 2n / [tex]^3log4[/tex] + 1
[tex]^{18}log75[/tex]
= [tex]^3log75 / ^3log18[/tex]
= [tex]^3log(3x5^2) / ^3log(3^2x2)[/tex]
= [tex]^3log3 + 2[/tex] x [tex]^3log5 / 2[/tex] x [tex]^3log3 + ^3log2[/tex]
= 1 + 2(n) / 2 x 1 + [tex]^3log2[/tex]
= 1 + 2n / 2 + [tex]^3log2[/tex]
Pelajari lebih lanjut
Pelajari lebih lanjut tentang logaritma pada https://brainly.co.id/tugas/35543073
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