Roboguru

3log36+3log15−9log625+3log121​− log0,017log3​×log2710log6​=...

Pertanyaan

3log36+3log159log625+3log121
log0,017log3×log2710log6=...  

Pembahasan Soal:

Ingat 

  • alogbc=alogb+alogc 
  • alogcb=alogbalogc 
  • aalogb=b 
  • blank to the power of a to the power of n log space b to the power of m equals m over n times blank to the power of a log space b 

Perhatikan perhitungan berikut 

3log36+3log159log625+3log121log0,017log3×log2710log6=3log36+3log153log(625)21+3log12127log3×3log36=3log6252136×15×121(2)×37×6=3log(54)2132×4×3×5×3×41(7)=3log(5232×5)(7)=73log(532)=7(3log323log5)=7(23log5)=14+73log5   

Dengan demikian,

 3log36+3log159log625+3log121log0,017log3×log2710log6=14+73log5

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Lestari

Mahasiswa/Alumni Universitas Sebelas Maret

Terakhir diupdate 13 September 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Tentukan nilai logaritma 9log25⋅5log2−3log54!

Pembahasan Soal:

Ingat sifat bentuk logaritma di bawah ini:

alog(bc)=alogb+alogc

alogbblogc=alogc

alogbm=m(alogb)

Dengan sifat di atas, maka diperoleh nilai dari

9log255log23log54=32log525log23log(227)=223log55log2(3log2+3log27)=3log23log23log33=033log3=31=3

Jadi, nilai 9log255log23log54 adalah 3.

0

Roboguru

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

Pembahasan Soal:

Ingat sifat logaritma 

anlogbmalogb+alogcalogbalogcalogcalogb====nmalogbalogbcalogcbclogb

dengan a,b,c0dana=1.

Ingat juga faktor dari selisih bilangan kuadrat (x2y2)=(x+y)(xy). Sehingga bisa dilakukan operasi sebagai berikut:

(3log18)2(3log2)23log6========(3log18+3log2)(3log183log2)3log621(3log182)(3log218)3log621(3log36)(3log9)3log621(3log62)(3log32)3log62123log623log6213log643log621=64log621214181

Dengan demikian, Nilai dari (3log18)2(3log2)23log6=81.

0

Roboguru

Jika , maka nilai dari  adalah ....

Pembahasan Soal:

Ingat bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a to the power of n end presuperscript b to the power of m end cell equals cell m over n times log presuperscript a b end cell row cell log presuperscript a b plus log presuperscript a c end cell equals cell log presuperscript a open parentheses b cross times c close parentheses end cell row cell log presuperscript a b minus log presuperscript a c end cell equals cell log presuperscript a open parentheses b over c close parentheses end cell end table end style

dengan undefined, undefinedundefined, serta undefined dan undefined.

Oleh karena itu didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell log presuperscript 1 fourth end presuperscript 1 over 36 plus log presuperscript 2 12 minus log presuperscript 8 27 end cell row blank equals cell log presuperscript 1 over 2 squared end presuperscript 1 over 6 squared plus log presuperscript 2 12 minus log presuperscript 2 cubed end presuperscript 3 cubed end cell row blank equals cell log presuperscript 2 to the power of negative 2 end exponent end presuperscript 6 to the power of negative 2 end exponent plus log presuperscript 2 12 minus 3 over 3 times log presuperscript 2 3 end cell row blank equals cell fraction numerator negative 2 over denominator negative 2 end fraction times log presuperscript 2 6 plus log presuperscript 2 12 minus log presuperscript 2 3 end cell row blank equals cell log presuperscript 2 6 plus log presuperscript 2 12 minus log presuperscript 2 3 end cell row blank equals cell log presuperscript 2 open parentheses fraction numerator 6 cross times 12 over denominator 3 end fraction close parentheses end cell row blank equals cell log presuperscript 2 24 end cell row blank equals cell log presuperscript 2 open parentheses 8 cross times 3 close parentheses end cell row blank equals cell log presuperscript 2 8 plus log presuperscript 2 3 end cell row blank equals cell 3 plus log presuperscript 2 3 end cell end table end style

Diketahui begin mathsize 14px style log presuperscript 1 fourth end presuperscript 1 over 36 plus log presuperscript 2 12 minus log presuperscript 8 27 equals x plus log presuperscript y x end style, maka dapat kita simpulkan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row x equals 3 row y equals 2 end table end style

Dengan demikian, nilai dari undefined adalah begin mathsize 14px style open parentheses 3 close parentheses open parentheses 2 close parentheses equals 6 end style.

Jadi, jawaban yang tepat adalah C.

0

Roboguru

...

Pembahasan Soal:

Perlu diingat bahwa:

open parentheses a to the power of b close parentheses to the power of c equals a to the power of b times c end exponent log presuperscript a to the power of m end presuperscript space b to the power of n equals n over m times scriptbase log space b end scriptbase presuperscript a log presuperscript a space b to the power of c equals c times log presuperscript a space b a to the power of log presuperscript a space b end exponent equals b 

Perhatikan perhitungan berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 3 close parentheses to the power of log presuperscript 9 space open parentheses x minus 1 close parentheses squared end exponent end cell equals cell open parentheses 3 to the power of begin inline style 1 half end style end exponent close parentheses to the power of log presuperscript 9 space open parentheses x minus 1 close parentheses squared end exponent end cell row blank equals cell open parentheses 3 to the power of begin inline style 1 half end style end exponent close parentheses to the power of log presuperscript 3 squared end presuperscript space open parentheses x minus 1 close parentheses squared end exponent end cell row blank equals cell open parentheses 3 to the power of begin inline style 1 half end style end exponent close parentheses to the power of begin inline style 2 over 2 end style times log presuperscript 3 space open parentheses x minus 1 close parentheses end exponent end cell row blank equals cell open parentheses 3 to the power of begin inline style 1 half end style end exponent close parentheses to the power of begin inline style log presuperscript 3 space open parentheses x minus 1 close parentheses end style end exponent end cell row blank equals cell 3 to the power of begin inline style 1 half end style times begin inline style blank presuperscript 3 end style begin inline style log end style begin inline style space end style begin inline style open parentheses x minus 1 close parentheses end style end exponent end cell row blank equals cell 3 to the power of log presuperscript 3 space open parentheses x minus 1 close parentheses to the power of 1 half end exponent end exponent end cell row blank equals cell begin inline style 3 to the power of log presuperscript 3 space square root of x minus 1 end root end exponent end style begin inline style space end style end cell row blank equals cell begin inline style square root of x minus 1 end root end style end cell end table    

Sehingga, bentuk sederhana dari open parentheses square root of 3 close parentheses to the power of log presuperscript 9 space open parentheses x minus 1 close parentheses squared end exponent adalah square root of x minus 1 end root.

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Jika , maka

Pembahasan Soal:

Logaritma merupakan invers dari eksponen.

Jika a to the power of p equals b maka log presuperscript a space b equals p 

Ingat kembali sifat bentuk logaritma berikut ini.

  • a to the power of log presuperscript a space b end exponent equals b
     
  • scriptbase log space open parentheses b to the power of m close parentheses end scriptbase presuperscript a to the power of n end presuperscript equals m over n space open parentheses log presuperscript a space b close parentheses
     
  • scriptbase log space open parentheses b to the power of m close parentheses end scriptbase presuperscript a equals m space open parentheses log presuperscript a space b close parentheses 

Diketahui: 4 to the power of square root of 2 space log space x end exponent equals 81

Dengan definisi dan sifat logaritma di atas, diperoleh perhitungan berikut ini.

      table attributes columnalign right center left columnspacing 0px end attributes row cell 4 to the power of scriptbase log space end scriptbase presuperscript square root of 2 end presuperscript x end exponent end cell equals 81 row cell 4 to the power of scriptbase log space end scriptbase presuperscript 2 to the power of 1 half end exponent end presuperscript x end exponent end cell equals 81 row cell 4 times fraction numerator 1 over denominator begin display style bevelled 1 half end style end fraction to the power of scriptbase log space end scriptbase presuperscript 2 x end exponent end cell equals 81 row cell 8 to the power of scriptbase log space end scriptbase presuperscript 2 x end exponent end cell equals 81 row cell 2 to the power of 3 times scriptbase log space end scriptbase presuperscript 2 x end exponent end cell equals 81 row cell 2 to the power of scriptbase log space end scriptbase presuperscript 2 x cubed end exponent end cell equals 81 row cell x cubed end cell equals 81 row cell scriptbase log space 81 end scriptbase presuperscript x end cell equals 3 row cell scriptbase log space 3 to the power of 4 end scriptbase presuperscript x end cell equals 3 row cell fraction numerator 4 times scriptbase log space 3 end scriptbase presuperscript x over denominator 4 end fraction end cell equals cell 3 over 4 end cell row cell scriptbase log space 3 end scriptbase presuperscript x end cell equals cell 3 over 4 end cell end table    

Diperoleh Error converting from MathML to accessible text., sehingga Error converting from MathML to accessible text.:

    table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript x space 27 end cell equals cell log presuperscript x space 3 cubed end cell row blank equals cell 3 space open parentheses log presuperscript x space 3 close parentheses end cell row blank equals cell 3 times 3 over 4 end cell row blank equals cell 9 over 4 end cell row blank equals cell 2 comma 25 end cell end table  

Maka, Error converting from MathML to accessible text. 

Oleh karena itu, tidak ada jawaban yang tepat.

0

Roboguru

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