Roboguru

Pertanyaan

Nilai space dari space cubed log space 54 space plus space cubed log space 2 space long dash to the power of space 3 end exponent log space 4 long dash space cubed log space 9 space equals space.... space

  1. 1

  2. 2

  3. 3

  4. 5

  5. 6

Pembahasan Soal:

Gunakan space sifat minus sifat space logaritma comma space yaitu space colon space  to the power of a log space a to the power of n equals n space  to the power of a log space b space plus to the power of a log space C equals to the power of a log space b c  to the power of a log space b space minus to the power of a log space c equals to the power of a log space b over c space  cubed log space 54 space plus cubed log space 2 minus cubed log space 4 space minus cubed log space 9 space equals cubed log space fraction numerator 54.2 over denominator 9.4 end fraction space equals cubed log space 3 equals 1 space

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Intan

Mahasiswa/Alumni Institut Pertanian Bogor

Terakhir diupdate 04 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

5log20​(5log10)2−(5log2)2​=....

Pembahasan Soal:

Dengan menerapkan beberapa sifat logaritma maka dapat ditentukan:

table attributes columnalign right center left columnspacing 0px end attributes row p equals cell fraction numerator open parentheses log presuperscript 5 space 10 close parentheses squared minus open parentheses log presuperscript 5 space 2 close parentheses squared over denominator log presuperscript 5 space square root of 20 end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 5 space 10 minus log presuperscript 5 space 2 close parentheses open parentheses log presuperscript 5 space 10 plus log presuperscript 5 space 2 close parentheses over denominator log presuperscript 5 space 20 to the power of begin display style 1 half end style end exponent end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 5 space open parentheses begin display style 10 over 2 end style close parentheses close parentheses open parentheses log presuperscript 5 space open parentheses 10 times 2 close parentheses close parentheses over denominator begin display style 1 half end style times log presuperscript 5 space 20 end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 5 space 5 close parentheses up diagonal strike open parentheses log presuperscript 5 space 20 close parentheses end strike over denominator begin display style 1 half times up diagonal strike log presuperscript 5 space 20 end strike end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 1 half end style end fraction end cell row blank equals 2 end table  

Jadi, jawaban yang benar adalah C.

0

Roboguru

Pembahasan Soal:

l presuperscript 5 o g 25 plus to the power of 5 l o g 3 minus to the power of 5 l o g 15 equals to the power of 5 l o g space open parentheses fraction numerator 25 cross times 3 over denominator 15 end fraction close parentheses  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals to the power of 5 l o g space 5  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1

0

Roboguru

Nilai (3log18)2−(3log2)23log6​​ adalah ...

Pembahasan Soal:

Ingat sifat-sifat logaritma:

  1. log presuperscript straight a space straight a equals 1
  2. log presuperscript straight a space straight a to the power of straight m equals straight m
  3. log presuperscript straight a space straight b plus log presuperscript straight a space straight c equals log presuperscript straight a space straight b times straight c
  4. log presuperscript straight a space straight b minus log presuperscript straight a space straight c equals log presuperscript straight a space straight b over straight c


Ingat juga bahwa bentuk straight a squared minus straight b squared equals open parentheses straight a plus straight b close parentheses open parentheses straight a minus straight b close parentheses.

Maka diperoleh:


fraction numerator log presuperscript 3 space square root of 6 over denominator left parenthesis log presuperscript 3 space 18 right parenthesis squared space minus space left parenthesis log presuperscript 3 space 2 right parenthesis squared end fraction equals fraction numerator log presuperscript 3 space 6 to the power of begin display style 1 half end style end exponent over denominator open parentheses log presuperscript 3 space 18 plus log presuperscript 3 space 2 close parentheses open parentheses log presuperscript 3 space 18 minus log presuperscript 3 space 2 close parentheses end fraction equals fraction numerator begin display style 1 half end style log presuperscript 3 space 6 over denominator open parentheses log presuperscript 3 space open parentheses 18 times 2 close parentheses close parentheses open parentheses log presuperscript 3 space open parentheses begin display style bevelled 18 over 2 end style close parentheses close parentheses end fraction equals 1 half times fraction numerator log presuperscript 3 space 6 over denominator open parentheses log presuperscript 3 space open parentheses 2 squared times 9 close parentheses close parentheses open parentheses log presuperscript 3 space 9 close parentheses end fraction equals 1 half times fraction numerator log presuperscript 3 space 6 over denominator open parentheses log presuperscript 3 space 2 squared plus log presuperscript 3 space 9 close parentheses open parentheses log presuperscript 3 space 3 squared close parentheses end fraction equals 1 half times fraction numerator log presuperscript 3 space 6 over denominator open parentheses 2 times log presuperscript 3 space 2 plus log presuperscript 3 space 3 squared close parentheses open parentheses 2 times log presuperscript 3 space 3 close parentheses end fraction equals 1 half times fraction numerator log presuperscript 3 space 6 over denominator open parentheses 2 times log presuperscript 3 space 2 plus 2 times log presuperscript 3 space 3 close parentheses times 2 end fraction equals 1 half times fraction numerator log presuperscript 3 space 6 over denominator 2 times 2 times open parentheses log presuperscript 3 space 2 plus log presuperscript 3 space 3 close parentheses end fraction equals 1 over 8 times fraction numerator log presuperscript 3 space 6 over denominator log presuperscript 3 space 6 end fraction equals 1 over 8


Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

Sederhanakan: a.  6log84−6log7+6log21​

Pembahasan Soal:

Ingat kembali sifat-sifat logaritma:

alogcbalog(b×c)aloga===alogbalogcalogb+alogc1 

Sehingga

6log846log7+6log21======(6log846log7)+6log216log784+6log216log12+6log216log(12×21)6log61 

Dengan demikian hasil dari 6log846log7+6log21 adalah 1.

0

Roboguru

2log50+2log8−2log100=...

Pembahasan Soal:

2log50+2log82log100======2log(52×2)+2log232log(52×22)(2log52+2log2)+(32log2)(22log5+22log2)(22log5+1)+(31)(22log5+21)22log5+1+322log5+24+26  

Dengan demikian,  2log50+2log82log100=6.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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