{"id":202352,"date":"2018-08-17T11:51:40","date_gmt":"2018-08-17T04:51:40","guid":{"rendered":"https:\/\/www.quipper.com\/id\/blog\/?p=202352"},"modified":"2021-11-24T21:48:21","modified_gmt":"2021-11-24T14:48:21","slug":"perbandingan-gempa-dengan-logaritma","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/perbandingan-gempa-dengan-logaritma\/","title":{"rendered":"Membandingkan Kekuatan Gempa Bumi Menggunakan Logaritma"},"content":{"rendered":"

\"\"<\/a><\/p>\n

Tahukah Quipperian, bahwa setiap bentuk operasi dalam matematika memiliki bentuk kebalikan atau inversinya? Misalnya saja operasi penjumlahan memiliki inversi berupa operasi pengurangan. Selanjutnya, operasi perkalian mempunyai operasi pembagian sebagai inversinya. Lalu, bagaimana dengan operasi pangkat atau eksponen? Rupanya, operasi inversi dari eksponen adalah logaritma, <\/span>lho<\/span><\/em>, Quipperian!<\/span><\/p>\n

1. Logaritma sebagai Invers dari Eksponen<\/strong><\/h2>\n

\"\"<\/a><\/p>\n

Logika pembandingnya seperti ini:<\/span><\/p>\n

a. Operasi pengurangan sebagai invers dari operasi penjumlahan<\/strong><\/span><\/p>\n

Contoh:<\/span><\/p>\n

Dua ditambah 3 sama dengan 5. Bentuk inversnya adalah 5 dikurang berapa supaya hasilnya sama dengan 2? Jawabannya adalah 3. Secara matematis:<\/span><\/p>\n

2 + 3 = 5 <\/span>\u2192<\/span> 2 = 5 – 3 <\/span><\/p>\n

b. Operasi logaritma sebagai invers dari operasi eksponen<\/strong><\/span><\/p>\n

Contoh:<\/span><\/p>\n

2<\/span>4<\/span><\/sup> = 16 <\/span>\u2192<\/span> 4 = <\/span>2<\/span><\/sup>log 16 (<\/span>2<\/span><\/sup>log 16 bisa juga dituliskan dalam bentuk log<\/span>2<\/span><\/sub> 16)<\/span><\/p>\n

Maka secara umum, hubungan antara eksponen dan logaritma dapat dinyatakan sebagai berikut:<\/span><\/p>\n

\"\"<\/a><\/p>\n

dengan syarat: a > 0; a \u2260 1, dan c > 0. Koefisien a dinamakan basis dan juga perlu diingat, biasanya basis 10 tidak dituliskan. Jadi, log<\/span>10<\/span><\/sub> x = log x.<\/span><\/p>\n

2. Sifat-Sifat Logaritma<\/strong><\/h2>\n

\"\"<\/a><\/p>\n

Selanjutnya, serupa dengan operasi penjumlahan yang memiliki sifat komutatif, asosiatif, dan distributif, operasi log juga memiliki sifat-sifat sebagai berikut:<\/span><\/p>\n

a. log\u00a0log<\/em>\u00a01<\/span> =0 <\/span><\/h3>\n

b. a\u00a0<\/em>= 1<\/h3>\n

c. xy<\/em> = x\u00a0<\/em><\/span>+\u00a0y<\/span><\/h3>\n

\"\"<\/a><\/p>\n

d. x\/y\u00a0= x<\/em><\/span>\u00a0– y<\/em><\/span><\/h3>\n

\"\"<\/a><\/p>\n

e. x<\/em>m<\/span><\/sup> =m.x<\/em><\/span><\/h3>\n

\"\"<\/a><\/p>\n

f. b<\/em> =\u00a0<\/span>b\/<\/span>a<\/span> <\/em>=\u00a0<\/span>1<\/span>\/<\/span>a<\/span><\/em><\/h3>\n

\"\"<\/a><\/p>\n

g. x<\/em> =\u00a0<\/span>x\/<\/span>a<\/span><\/em><\/h3>\n

h. b<\/em>m<\/span><\/sub><\/sup> =<\/span>m\/<\/span>n.<\/span>b<\/span><\/em><\/h3>\n

i. b.<\/em>c<\/span> = c<\/span><\/em><\/h3>\n

\"\"<\/a><\/p>\n

j. a<\/em>b<\/span><\/sup> = b<\/span><\/em><\/h3>\n

3. Membandingkan Kekuatan Gempa Bumi Menggunakan Logaritma<\/strong><\/h2>\n

\"\"<\/a><\/p>\n

Setelah memahami dasar perhitungan log, Quipperian mungkin berpikir tentang apa sebenarnya aplikasi nyata dari penggunaan log, terutama dalam kehidupan sehari-hari. Nah, tahukah Quipperian bahwa operator log ini memiliki kaitan yang erat dengan gempa bumi? Gempa bumi merupakan salah satu contoh gelombang, yaitu getaran yang merambat. Aktivitas getaran gempa bumi ini bisa direkam oleh alat yang bernama seismograf.<\/span><\/p>\n

Pada prinsipnya, seismograf terdiri dari gantungan pemberat dan ujung lancip seperti pensil. Dengan demikian, dapat terbaca kekuatan dan arah gempa melalui gambaran gerakan bumi yang tercatat. Semakin besar kekuatan gempanya, maka akan semakin besar amplitudo gelombang yang muncul dalam bentuk seismogram. <\/span><\/p>\n

Parameter yang harus diketahui adalah amplitudo maksimum gelombang gempa dan beda waktu tempuh antara gelombang primer dan gelombang sekunder (dalam detik) atau jarak antara seismometer dengan pusat gempa (dalam kilometer). <\/span><\/p>\n

Kekuatan gempa diukur menggunakan satuan skala Richter. Skala Richter didefinisikan sebagai logaritma basis 10 dari amplitudo maksimum, yang diukur dalam satuan mikrometer, dari rekaman seismometer pada jarak 100 km dari pusat gempa. Misalnya saja telah terekam peristiwa gempa bumi dari seismometer yang terpasang sejauh 100 km dari pusat gempa dengan amplitudo maksimum sebesar 1 mm (1000 mikrometer). Maka secara sederhana, besar kekuatan gempa tersebut adalah <\/span>log<\/span> 10<\/span>3<\/span> =3<\/span> SR.<\/span><\/p>\n

Karena secara matematis kekuatan gempa diukur menggunakan log, artinya kenaikan nilai pada skala Richter pun bersifat logaritmik. Misal gempa berkekuatan 1 SR setara dengan 10 ton bom TNT, maka gempa berkekuatan 2 SR tidak secara linear setara dengan 20 ton bom TNT melainkan setara dengan 100 ton bom TNT. <\/span><\/p>\n

Ya, kenaikan 1 nilai skala Richter artinya dampak kerusakan yang ditimbulkan menjadi 100 kali lebih besar, <\/span>lho<\/span><\/em>, Quipperian! Sebagai gambaran, gempa bumi berkekuatan 5 SR sudah mampu menghancurkan bangunan!<\/span><\/p>\n

Nah, jika Quipperian ingin mengetahui lebih dalam tentang aplikasi lain dari materi ini, kamu bisa mempelajarinya pada bidang Matematika melalui Quipper Video! Yuk, berlangganan dengan klik link di bawah ini! Selamat mendalami konsep matematika di keseharian kita, Quipperian!<\/span><\/p>\n

Link cara daftar: <\/span>bit.ly\/caradaftarquipper<\/span><\/a><\/p>\n

Link registrasi: <\/span>https:\/\/learn.quipper.com\/signup\/video\/ID<\/span><\/a><\/p>\n

Penulis: Laili Miftahur Rizqi <\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Tahukah Quipperian, bahwa setiap bentuk operasi dalam matematika memiliki bentuk kebalikan atau inversinya? Misalnya saja operasi penjumlahan memiliki inversi berupa operasi pengurangan. Selanjutnya, operasi…<\/p>\n","protected":false},"author":99400369,"featured_media":202872,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384888,679384865],"tags":[],"ppma_author":[679386827],"class_list":["post-202352","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mapel","category-matematika"],"acf":[],"yoast_head":"\nMembandingkan Kekuatan Gempa Bumi Menggunakan Logaritma<\/title>\n<meta name=\"description\" content=\"Quipperian, belajar logaritma lebih menyenangkan kalau sambil studi kasus. 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