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Jika 2logab2loga​=a31​loga dan bcloga=32​, maka nilai  adalah ....

Pertanyaan

Jika begin mathsize 14px style fraction numerator log presuperscript 2 space a over denominator log presuperscript 2 space a b end fraction equals log presuperscript a to the power of 1 third end exponent end presuperscript space a end style dan size 14px log presuperscript size 14px b size 14px c end presuperscript size 14px space size 14px a size 14px equals size 14px 2 over size 14px 3, maka nilai size 14px log presuperscript size 14px c size 14px space size 14px a size 14px b adalah .... 

  1. size 14px minus size 14px 6 

  2. size 14px minus size 14px 2 

  3. size 14px minus size 14px 1 over size 14px 2 

  4. size 14px minus size 14px 1 

  5. size 14px 2 

Pembahasan Video:

Pembahasan Soal:

Berdasarkan yang diketahui pada soal diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator log presuperscript 2 space a over denominator log presuperscript 2 space a b end fraction end cell equals cell log presuperscript a to the power of 1 third end exponent end presuperscript space a end cell row cell log presuperscript a b end presuperscript space a end cell equals 3 row cell log presuperscript a space a b end cell equals cell 1 third end cell row cell log presuperscript a space a plus log presuperscript a space b end cell equals cell 1 third end cell row cell 1 plus log presuperscript a space b end cell equals cell 1 third end cell row cell log presuperscript a space b end cell equals cell 1 third minus 1 end cell row cell log presuperscript a space b end cell equals cell negative 2 over 3 end cell end table end style  

selanjutnya dari begin mathsize 14px style log presuperscript b c end presuperscript space a equals 2 over 3 end style diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a space b c end cell equals cell 3 over 2 end cell row cell log presuperscript a space b plus log presuperscript a space c end cell equals cell 3 over 2 end cell row cell negative 2 over 3 plus log presuperscript a space c end cell equals cell 3 over 2 end cell row cell log presuperscript a space c end cell equals cell 3 over 2 plus 2 over 3 end cell row cell log presuperscript a space c end cell equals cell 13 over 6 end cell end table end style  

sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript c space a b end cell equals cell fraction numerator log presuperscript a space a b over denominator log presuperscript a space c end fraction end cell row blank equals cell fraction numerator log presuperscript a space a plus log presuperscript a space b over denominator log presuperscript a space c end fraction end cell row blank equals cell fraction numerator 1 minus begin display style 2 over 3 end style over denominator begin display style 13 over 6 end style end fraction end cell row blank equals cell fraction numerator begin display style 1 third end style over denominator begin display style 13 over 6 end style end fraction end cell row blank equals cell 2 over 13 end cell end table end style  

Dengan demikian diperoleh nilai dari begin mathsize 14px style log presuperscript c space a b equals 2 over 13 end style.

Jadi, tidak ada jawaban yang benar.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 14 Oktober 2021

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Pertanyaan yang serupa

log221​log25−log22​=…

Pembahasan Soal:

Ingat!

Sifat Logaritma:
log presubscript space presuperscript a space b plus log presubscript space presuperscript a space c equals log presubscript space presuperscript a space left parenthesis b. c right parenthesis  log presubscript space presuperscript a space b minus log presubscript space presuperscript a space c equals log presubscript space presuperscript a space open parentheses b over c close parentheses  a squared minus b squared equals left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis  log presubscript space presuperscript space space x equals log presubscript space presuperscript 10 space x  log presubscript space presuperscript space space 10 equals 1  fraction numerator log presubscript space presuperscript p space b over denominator log presubscript space presuperscript p space c end fraction equals log presubscript space presuperscript c space b  log presubscript space presuperscript a space a equals 1

Maka:

Soal Seharusnya Seperti ini:

fraction numerator log squared space 5 minus log squared space 2 over denominator log space 2 1 half end fraction equals fraction numerator open parentheses log space 5 plus log space 2 close parentheses open parentheses log space 5 minus log space 2 close parentheses over denominator log space 2 1 half end fraction  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 fraction numerator log left parenthesis 5.2 right parenthesis log space open parentheses 5 over 2 close parentheses over denominator log space 5 over 2 end fraction  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 fraction numerator log space 10. log space 5 over 2 over denominator log space 5 over 2 end fraction  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 fraction numerator 1. log space 5 over 2 over denominator log space 5 over 2 end fraction  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 log presubscript space presuperscript 5 over 2 end presuperscript space 5 over 2  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 space 1

0

Roboguru

Bentuk sederhana dari  = ...

Pembahasan Soal:

Sifat-sifat logaritma:

  • begin mathsize 12px style a to the power of n log b equals 1 over n times log presuperscript a b end style
  • begin mathsize 12px style log presuperscript a b equals fraction numerator log b over denominator log a end fraction end style
  • begin mathsize 12px style log presuperscript a b minus log presuperscript a c equals log presuperscript a open parentheses b over c close parentheses end style
  • begin mathsize 12px style log presuperscript a b to the power of m equals m times log presuperscript a b end style
  • begin mathsize 12px style log presuperscript a a equals 1 end style

begin mathsize 12px style fraction numerator log presuperscript square root of 3 end presuperscript 100 minus log 9 minus log presuperscript 5 625 over denominator log presuperscript 2 12 minus log presuperscript 2 3 end fraction  equals fraction numerator log presuperscript open parentheses 3 close parentheses to the power of 1 half end exponent end presuperscript 100 times log 9 minus log presuperscript 5 5 to the power of 4 over denominator log presuperscript 2 open parentheses begin display style 12 over 3 end style close parentheses end fraction  equals fraction numerator 2 times log presuperscript 3 100 times log 9 minus 4 times log presuperscript 5 5 over denominator log presuperscript 2 4 end fraction  equals fraction numerator log presuperscript 3 100 squared times log 9 minus 4 over denominator log presuperscript 2 2 squared end fraction  equals fraction numerator begin display style fraction numerator log 10 to the power of 4 times log 9 over denominator log 3 end fraction end style minus 4 over denominator 2 times log presuperscript 2 2 end fraction  equals fraction numerator log 10 to the power of 4 times log presuperscript 3 9 minus 4 over denominator 2 end fraction  equals fraction numerator log 10 to the power of 4 times log presuperscript 3 3 squared minus 4 over denominator 2 end fraction  equals fraction numerator 4 times 2 times log presuperscript 3 3 minus 4 over denominator 2 end fraction  equals fraction numerator 8 minus 4 over denominator 2 end fraction  equals 4 over 2  equals 2 end style

Jadi, begin mathsize 12px style fraction numerator log presuperscript square root of 3 end presuperscript 100 minus log 9 minus log presuperscript 5 625 over denominator log presuperscript 2 12 minus log presuperscript 2 3 end fraction end style = 2.

0

Roboguru

Jika a=6log5 dan b=5log4, tentukan nilai 4log0,24 dalam a dan b.

Pembahasan Soal:

Ingat kembali sifat bentuk logaritma berikut:

log presuperscript a space a equals 1 log presuperscript a space b equals fraction numerator log presuperscript p space b over denominator log presuperscript p space a end fraction log presuperscript a space b times log presuperscript b space c equals log presuperscript a space c log presuperscript a space b to the power of m equals m times log presuperscript a space b log presuperscript a space open parentheses b over c close parentheses equals log presuperscript a space b minus log presuperscript a space c  

Maka:

begin mathsize 14px style log presuperscript 4 space 0 comma 24 equals fraction numerator log presuperscript 6 space 0 comma 24 over denominator log presuperscript 6 space 4 end fraction space space space space space space space space space space space space space space equals fraction numerator log presuperscript 6 space begin display style 24 over 100 end style over denominator log presuperscript 6 space 5 times log presuperscript 5 space 4 end fraction space space space space space space space space space space space space space space equals fraction numerator log presuperscript 6 space begin display style 6 over 25 end style over denominator log presuperscript 6 space 5 times log presuperscript 5 space 4 end fraction space space space space space space space space space space space space space space equals fraction numerator log presuperscript 6 space 6 minus log presuperscript 6 space 25 over denominator log presuperscript 6 space 5 times log presuperscript 5 space 4 end fraction space space space space space space space space space space space space space space equals fraction numerator 1 minus log presuperscript 6 space 5 squared over denominator log presuperscript 6 space 5 times log presuperscript 5 space 4 end fraction space space space space space space space space space space space space space space equals fraction numerator 1 minus 2 space log presuperscript 6 space 5 over denominator log presuperscript 6 space 5 times log presuperscript 5 space 4 end fraction space space space space space space space space space space space space space space equals fraction numerator 1 minus 2 a over denominator a b end fraction end style 

Jadi, log presuperscript 4 space 0 comma 24 equals fraction numerator 1 minus 2 a over denominator a b end fraction.

0

Roboguru

Hasil dari  adalah ...

Pembahasan Soal:

Ingat bahwa Error converting from MathML to accessible text. , maka


Error converting from MathML to accessible text. 

Jadi, hasil dari undefined adalah Error converting from MathML to accessible text.

Maka jawaban yang tepat adalah B.

0

Roboguru

Nilai dari   adalah ....

Pembahasan Soal:

Ingat bahwa bentuk umum logaritma adalah l presuperscript a o g invisible function application b equals c left right arrow a to the power of c equals b comma dengan a comma space b greater than 0 dan a not equal to 1.

Kemudian, ingat beberapa sifat logaritma berikut ini.

table attributes columnalign right center left columnspacing 0px end attributes row cell blank to the power of a l o g blank a end cell equals cell 1 to the power of a to the power of n end exponent log invisible function application b to the power of m equals m over n times to the power of a log invisible function application b to the power of a log invisible function application b equals fraction numerator blank to the power of x log invisible function application b over denominator blank to the power of x log invisible function application a end fraction end cell row cell space to the power of a log invisible function application b plus scriptbase log c end scriptbase presuperscript a end cell equals cell scriptbase log open parentheses b times c close parentheses end scriptbase presuperscript a to the power of a log invisible function application b minus scriptbase log c end scriptbase presuperscript a equals scriptbase log open parentheses b over c close parentheses end scriptbase presuperscript a end cell end table

Dapat diperhatikan bahwa p squared minus q squared equals open parentheses p plus q close parentheses open parentheses p minus q close parentheses.

Oleh karena itu, nilai dari fraction numerator open parentheses log presuperscript a a b close parentheses squared minus open parentheses log presuperscript a b close parentheses squared over denominator blank to the power of a log invisible function application square root of a b squared end root end fraction dapat dihitung sebagai berikut.

fraction numerator open parentheses scriptbase log a b end scriptbase presuperscript a close parentheses squared minus open parentheses scriptbase log b end scriptbase presuperscript a close parentheses squared over denominator scriptbase log square root of a b squared end root end scriptbase presuperscript a end fraction equals fraction numerator open parentheses scriptbase log a b end scriptbase presuperscript a plus scriptbase log b end scriptbase presuperscript a close parentheses open parentheses scriptbase log a b end scriptbase presuperscript a minus scriptbase log b end scriptbase presuperscript a close parentheses over denominator blank to the power of a log invisible function application open parentheses a b squared close parentheses to the power of 1 half end exponent end fraction  equals fraction numerator open parentheses scriptbase log open parentheses a b times b close parentheses end scriptbase presuperscript a close parentheses open parentheses scriptbase log open parentheses begin display style fraction numerator a b over denominator b end fraction end style close parentheses end scriptbase presuperscript a close parentheses over denominator blank to the power of a log invisible function application open parentheses a b squared close parentheses to the power of 1 half end exponent end fraction equals fraction numerator open parentheses scriptbase log open parentheses a b squared close parentheses end scriptbase presuperscript a close parentheses open parentheses scriptbase log a end scriptbase presuperscript a close parentheses over denominator blank to the power of a log invisible function application open parentheses a b squared close parentheses to the power of 1 half end exponent end fraction equals fraction numerator open parentheses scriptbase log open parentheses a b squared close parentheses end scriptbase presuperscript a close parentheses times 1 over denominator blank to the power of a log invisible function application open parentheses a b squared close parentheses to the power of 1 half end exponent end fraction equals fraction numerator scriptbase log open parentheses a b squared close parentheses end scriptbase presuperscript a over denominator blank to the power of a log invisible function application open parentheses a b squared close parentheses to the power of 1 half end exponent end fraction equals blank to the power of open parentheses a b squared close parentheses to the power of 1 half end exponent end exponent log invisible function application open parentheses a b squared close parentheses equals fraction numerator 1 over denominator 1 half end fraction times open parentheses scriptbase log open parentheses a b squared close parentheses end scriptbase presuperscript a b squared end presuperscript close parentheses equals 2 times 1 equals 2

Dengan demikian, nilai dari fraction numerator open parentheses log presuperscript a a b close parentheses squared minus open parentheses log presuperscript a b close parentheses squared over denominator blank to the power of a log invisible function application square root of a b squared end root end fraction adalah 2.

Jadi, jawaban yang tepat adalah B.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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