Roboguru
SD

Hitung nilai dari ekspresi, log(tan 5∘)+log(tan 6∘)+log(tan 7∘)+...+log(tan 85∘).

Pertanyaan

Hitung nilai dari ekspresi, begin mathsize 12px style log left parenthesis tan space 5 degree right parenthesis plus log left parenthesis tan space 6 degree right parenthesis plus log left parenthesis tan space 7 degree right parenthesis plus... plus log left parenthesis tan space 85 degree right parenthesis end style.

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai dari ekspresi dari begin mathsize 12px style log left parenthesis tan space 5 degree right parenthesis plus log left parenthesis tan space 6 degree right parenthesis plus log left parenthesis tan space 7 degree right parenthesis plus... plus log left parenthesis tan space 85 degree right parenthesis end style adalah 0.

Pembahasan

Ingat!

Sifat logaritma:

  • log presuperscript a space b plus log presuperscript a space c equals log presuperscript a open parentheses b cross times c close parentheses 
  • log presuperscript a space 1 equals 0

Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell log left parenthesis tan space 5 degree right parenthesis plus log left parenthesis tan space 6 degree right parenthesis plus log left parenthesis tan space 7 degree right parenthesis plus... plus log left parenthesis tan space 85 degree right parenthesis end cell row blank equals cell log left parenthesis tan space 5 degree times tan space 85 degree times tan space 6 degree times tan space 84 degree times tan space 7 degree times tan space 83 degree space... right parenthesis end cell row blank equals cell log left parenthesis tan space 5 degree times tan space left parenthesis 90 degree minus 5 degree right parenthesis times tan space 6 degree times tan left parenthesis 90 degree minus 6 degree right parenthesis space.... right parenthesis end cell row blank equals cell log left parenthesis tan space 5 degree times cot space 5 degree times tan space 6 degree times cot space 6 degree space... right parenthesis end cell row blank equals cell log left parenthesis 1 cross times 1 cross times 1 space... right parenthesis end cell row blank equals cell log space 1 end cell row blank equals 0 end table end style  

Jadi, nilai dari ekspresi dari begin mathsize 12px style log left parenthesis tan space 5 degree right parenthesis plus log left parenthesis tan space 6 degree right parenthesis plus log left parenthesis tan space 7 degree right parenthesis plus... plus log left parenthesis tan space 85 degree right parenthesis end style adalah 0.

24

0.0 (0 rating)

Pertanyaan serupa

Nilai x yang memenuhi persamaan 4⋅3log(x2−3)−91​log(x2−3)=0 adalah ....

23

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia