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Nilai dari  adalah ...

Pertanyaan

Nilai dari log subscript 2 space 24 minus log subscript 2 space 3 plus log subscript 3 space 12 plus log subscript 3 space 1 fourth adalah ...begin mathsize 14px style space end style 

  1. 6space 

  2. 7space 

  3. 5space 

  4. 4space 

  5. 3space 

Pembahasan Soal:

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row cell log subscript a space b end cell equals cell c left right arrow a to the power of c equals b end cell row cell log subscript a space open parentheses b over c close parentheses end cell equals cell log subscript a space b minus log subscript a space c end cell row cell log subscript a open parentheses b times c close parentheses end cell equals cell log subscript a space b plus log subscript a space c end cell end table  

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell log subscript 2 space 24 minus log subscript 2 space 3 plus log subscript 3 space 12 plus log subscript 3 space 1 fourth end cell row blank equals cell open parentheses log subscript 2 space 24 minus log subscript 2 space 3 close parentheses plus open parentheses log subscript 3 space 12 plus log subscript 3 space 1 fourth close parentheses end cell row blank equals cell log subscript 2 space 24 over 3 plus log subscript 3 space 12 times 1 fourth end cell row blank equals cell log subscript 2 space 8 plus log subscript 3 space 3 end cell row blank equals cell 3 plus 1 end cell row blank equals 4 end table 

Sehingga, Error converting from MathML to accessible text..

Jadi, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni Universitas Indraprasta PGRI

Terakhir diupdate 01 Mei 2021

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Pertanyaan yang serupa

Nilai dari

Pembahasan Soal:

Sifat-sifat logaritma sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a space b c end cell equals cell log presuperscript a space b plus log presuperscript a space c end cell row cell log presuperscript a space b over c end cell equals cell log presuperscript a space b minus log presuperscript a space c end cell end table

Sehingga,

log presuperscript 5 space 4 minus log presuperscript 5 space 24 plus log presuperscript 5 space 150 equals log presuperscript 5 space 4 over 24 times 150 equals log presuperscript 5 space 25 equals 2

Jadi, nilai dari log presuperscript 5 space 4 minus log presuperscript 5 space 24 plus log presuperscript 5 space 150 equals 2.

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Roboguru

Hasil dari

Pembahasan Soal:

Sebelum menjawab soal tersebut, maka kita harus mengetahui sifat-sifat logaritma sebagai berikut:

1. begin mathsize 14px style blank to the power of a log space b plus to the power of a log space c equals to the power of a log space b times c end style 

2. begin mathsize 14px style blank to the power of a log space b minus to the power of a log space c equals to the power of a log space b over c end style 

3. begin mathsize 14px style blank to the power of a log space b times to the power of b log space c equals to the power of a log space c end style 

4. begin mathsize 14px style blank to the power of a to the power of m end exponent log space b to the power of n equals n over m to the power of a log space b end style 

5. begin mathsize 14px style blank to the power of a log space a equals 1 end style 

sehingga hasil dari

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator blank cubed log space 5. to the power of square root of 5 end exponent log space 9 plus to the power of 8 log space 2 over denominator blank squared log space 12 minus squared log space 3 end fraction end cell row blank equals cell fraction numerator blank cubed log space 5. to the power of 5 to the power of begin display style 1 half end style end exponent end exponent log space 3 squared plus to the power of 2 cubed end exponent log space 2 over denominator blank squared log space begin display style 12 over 3 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 over denominator begin display style bevelled 1 half end style end fraction end style cubed log space 5. to the power of 5 log space 3 plus begin display style 1 third end style squared log space 2 over denominator blank squared log space begin display style 2 squared end style end fraction end cell row blank equals cell fraction numerator begin display style 4 times cubed log space 3 plus 1 third squared log space 2 end style over denominator 2 times squared log space begin display style 2 end style end fraction end cell row blank equals cell fraction numerator 4 plus begin display style 1 third end style over denominator 2 end fraction end cell row blank equals cell fraction numerator begin display style 13 over 3 end style over denominator 2 end fraction end cell row blank equals cell 13 over 6 end cell end table end style 

 

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Roboguru

Nilai dari

Pembahasan Soal:

Error converting from MathML to accessible text.

0

Roboguru

Nilai  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.

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Roboguru

Diketahui 2log5=adan 3log5=b, maka nilai dari 5log256​adalah ....

Pembahasan Soal:

Dengan menggunakan sifat-sifat logaritma didapatkan

5log256======5log65log255log(2×3)5log525log2+5log322log51+3log512a1+b12aba+b2ab

Dengan demikian, 5log256=aba+b2ab.

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Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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