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Nilai dari 34log3+2log20−2log10 adalah ...

Pertanyaan

Nilai dari 34log3+2log202log10 adalah ...

  1. 5 

  2. 4 

  3. 1 

  4. 45 

  5. 54 

Pembahasan Soal:

Ingat kembali sifat-sifat logaritma:

alog(cb)anlogbmaloga===alogbalogcnmalogb1  

Sehingga

34log3+2log202log10======34log3+2log1020413log3+2log2411+141+114145  

Nilai dari 34log3+2log202log10 adalah 45

Oleh karena itu, jawaban yang benar adalah D. 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Amamah

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 12 September 2021

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Pertanyaan yang serupa

Bentuk sederhana dari  adalah ...

Pembahasan Soal:

Untuk menyelesaikan soal tersebut ingat sifat-sifat berikut.

  • scriptbase log invisible function application b to the power of m end scriptbase presuperscript a to the power of n end presuperscript equals m over n times scriptbase log invisible function application b end scriptbase presuperscript a
  • scriptbase log invisible function application b end scriptbase presuperscript a times scriptbase log invisible function application c end scriptbase presuperscript b equals scriptbase log invisible function application c end scriptbase presuperscript a
  • scriptbase log invisible function application a end scriptbase presuperscript a equals 1
  • scriptbase log invisible function application b end scriptbase presuperscript a minus scriptbase log invisible function application c end scriptbase presuperscript a equals scriptbase log invisible function application b over c end scriptbase presuperscript a

Sehingga akan didapatkan

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses log invisible function application x close parentheses squared minus open parentheses log invisible function application y close parentheses squared over denominator scriptbase log invisible function application 4 end scriptbase presuperscript 125 times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus scriptbase log invisible function application 9 end scriptbase presuperscript 8 times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction end cell equals cell fraction numerator left parenthesis log invisible function application x plus log invisible function application y right parenthesis left parenthesis log invisible function application x minus log invisible function application y right parenthesis over denominator scriptbase log invisible function application 2 squared end scriptbase presuperscript 5 cubed end presuperscript times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus scriptbase log invisible function application 3 squared end scriptbase presuperscript 2 cubed end presuperscript times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 scriptbase log invisible function application 2 end scriptbase presuperscript 5 times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus 2 over 3 scriptbase log invisible function application 3 end scriptbase presuperscript 2 times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 scriptbase log invisible function application 5 end scriptbase presuperscript 5 times log invisible function application x minus 2 over 3 scriptbase log invisible function application 2 end scriptbase presuperscript 2 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 times 1 times log invisible function application x minus 2 over 3 times 1 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 times log invisible function application x minus 2 over 3 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 left parenthesis log invisible function application x minus log invisible function application y right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 open parentheses log invisible function application open parentheses x over y close parentheses close parentheses end fraction end cell row blank equals cell fraction numerator log invisible function application left parenthesis x y right parenthesis over denominator 2 over 3 end fraction end cell row blank equals cell 3 over 2 log invisible function application left parenthesis x y right parenthesis end cell end table end style

Jadi, dapat disimpulkan bahwa bentuk sederhana dari fraction numerator open parentheses log invisible function application x close parentheses squared minus open parentheses log invisible function application y close parentheses squared over denominator scriptbase log invisible function application 4 end scriptbase presuperscript 125 times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus scriptbase log invisible function application 9 end scriptbase presuperscript 8 times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction adalah 3 over 2 log invisible function application left parenthesis x y right parenthesis.

Oleh karena itu, jawaban yang benar adalah C.

0

Roboguru

Nilai dari

Pembahasan Soal:

log presuperscript straight a space xy space equals space log presuperscript straight a space straight x plus log presuperscript straight a space straight y  log presuperscript straight a space straight x over straight y space equals space log presuperscript straight a space straight x minus log presuperscript straight a space straight y  log presuperscript 2 space 4 plus space log presuperscript 2 space 12 minus log presuperscript 2 space 6 space equals space log presuperscript 2 space fraction numerator 4.12 over denominator 6 end fraction  equals log presuperscript 2 space 8  equals log presuperscript 2 space 2 cubed  equals 3

0

Roboguru

Nilai dari

Pembahasan Soal:

Sifat-sifat yang digunakan:

log presuperscript straight a space straight b space space plus space log presuperscript straight a space straight c space equals space log presuperscript straight a space left parenthesis straight b. straight c right parenthesis  log presuperscript straight a space straight b space minus space log presuperscript straight a space straight c space equals space log presuperscript straight a space straight b over straight c  log presuperscript straight a space straight b to the power of straight n equals straight n space log presuperscript straight a space straight b  log presuperscript straight a space straight a space equals space 1    log presuperscript 2 space 6 space plus space log presuperscript 2 space 8 space minus space log presuperscript 2 space 12 space equals space log presuperscript 2 space open parentheses fraction numerator 6.8 over denominator 12 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 space space space space equals space log presuperscript 2 space 4  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 space space space space equals space log presuperscript 2 space 2 squared  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 space space space space equals space 2. space log presuperscript 2 space 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 space space space space space space space space space space space space space space space space space space equals space 2.1 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 space space space space space equals space 2

0

Roboguru

Bentuk  dapat disederhanakan menjadi ...

Pembahasan Soal:

Perlu diingat bahwa:

scriptbase log space b equals scriptbase log space b to the power of begin inline style 1 over m end style end exponent equals 1 over m times end scriptbase presuperscript a end scriptbase presuperscript a to the power of m end presuperscript scriptbase log space b end scriptbase presuperscript a Jika space a greater than 0 comma space a not equal to 1 comma space f left parenthesis x right parenthesis greater than 0 space dan space g left parenthesis x right parenthesis greater than 0 space space maka colon log presuperscript a space open square brackets fraction numerator f open parentheses x close parentheses over denominator g left parenthesis x right parenthesis end fraction close square brackets equals log presuperscript a space f left parenthesis x right parenthesis minus log presuperscript a space g left parenthesis x right parenthesis 

Perhatikan perhitungan berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space open parentheses 2 x minus 3 close parentheses minus log presuperscript 4 space open parentheses x minus 3 over 2 close parentheses end cell equals cell log presuperscript 2 space open parentheses 2 x minus 3 close parentheses minus log presuperscript 2 squared end presuperscript space open parentheses x minus 3 over 2 close parentheses end cell row blank equals cell log presuperscript 2 space open parentheses 2 x minus 3 close parentheses minus log presuperscript 2 space open parentheses x minus 3 over 2 close parentheses to the power of begin inline style 1 half end style end exponent end cell row blank equals cell log presuperscript 2 space open parentheses 2 x minus 3 close parentheses minus log presuperscript 2 space square root of x minus 3 over 2 end root end cell row blank equals cell log presuperscript 2 space open parentheses fraction numerator 2 x minus 3 over denominator square root of x minus 3 over 2 end root end fraction close parentheses end cell end table 

Sehingga, bentuk log presuperscript 2 space open parentheses 2 x minus 3 close parentheses minus log presuperscript 4 space open parentheses x minus 3 over 2 close parentheses dapat disederhanakan menjadi log presuperscript 2 space open parentheses fraction numerator 2 x minus 3 over denominator square root of x minus 3 over 2 end root end fraction close parentheses.

Jadi, jawaban yang tepat adalah C.

0

Roboguru

4. 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

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