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Diketahui alogcb​=p dan alogbc2=q, maka alogb=...

Pertanyaan

Diketahui alogcb=p dan alogbc2=q, maka alogb=... 

  1. 3qp 

  2. 3q2p

  3. 3q+p 

  4. 3q+2p

  5. 3p2p 

Pembahasan Soal:

Ingat!

Sifat-sifat logaritma:

  • alogb+alogc=alog(bc) 
  • alogbalogc=alogcb 
  • alogbn=nalogb 

Diketahui alogcb=p dan alogbc2=q, maka:

alogcbalogbalogc==pp...(1) 

alogbc2alogb+alogc2alogb+2alogc===qqq...(2) 

Eliminasi (1) dan (2) sehingga:

alogbalogc=palogb+2alogc=q×2×12alogb2alogc=2palogb+2alogc=q+3alogb=2p+qalogb=32p+q 

Oleh karena itu, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Sutiawan

Mahasiswa/Alumni Universitas Pasundan

Terakhir diupdate 12 September 2021

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Nilai dari ....

Pembahasan Soal:

size 14px log presuperscript size 14px 5 size 14px space size 14px 25 size 14px plus size 14px log presuperscript size 14px 5 size 14px space size 14px 3 size 14px minus size 14px log presuperscript size 14px 5 size 14px space size 14px 15 size 14px equals size 14px log presuperscript size 14px 5 open parentheses fraction numerator size 14px 25 size 14px cross times size 14px 3 over denominator size 14px 15 end fraction close parentheses size 14px equals size 14px log presuperscript size 14px 5 size 14px space size 14px 5 size 14px equals size 14px 1

0

Roboguru

Pembahasan Soal:

Ingat kembali sifat bentuk logaritma berikut ini.

  • log presuperscript a space open parentheses b to the power of m close parentheses equals m space open parentheses log presuperscript a space b close parentheses  
  • log presuperscript a space open parentheses b over c close parentheses equals log presuperscript a space b minus log presuperscript a space c 
  • log presuperscript a space b c equals log presuperscript a space b plus log presuperscript a space c 
  • log presuperscript a space a equals 1  

Dengan sifat  bentuk logaritma di atas, didapat perhitungan berikut ini.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open parentheses log presuperscript 6 space 9 square root of 2 close parentheses squared minus open parentheses log presuperscript 6 space 4 square root of 3 close parentheses squared over denominator log presuperscript 6 space 3 begin display style 3 over 8 end style end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 6 space 9 square root of 2 plus log presuperscript 6 space 4 square root of 3 close parentheses open parentheses log presuperscript 6 space 9 square root of 2 minus log presuperscript 6 space 4 square root of 3 close parentheses over denominator log presuperscript 6 space begin display style 27 over 8 end style end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 6 space open parentheses 9 square root of 2 times space 4 square root of 3 close parentheses close parentheses open parentheses log presuperscript 6 space open parentheses begin display style fraction numerator 9 square root of 2 over denominator 4 square root of 3 end fraction end style close parentheses close parentheses over denominator log presuperscript 6 space begin display style 27 over 8 end style end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 6 space open parentheses 36 square root of 6 close parentheses close parentheses open parentheses log presuperscript 6 space open parentheses begin display style fraction numerator 9 square root of 2 over denominator 4 square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction end style close parentheses close parentheses over denominator log presuperscript 6 space begin display style 27 minus end style log presuperscript 6 space 8 end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 6 space open parentheses 6 squared times 6 to the power of begin display style 1 half end style end exponent close parentheses close parentheses open parentheses log presuperscript 6 space open parentheses begin display style fraction numerator 9 square root of 2 square root of 3 over denominator 12 end fraction end style close parentheses close parentheses over denominator 3 space log presuperscript 6 space begin display style 3 minus end style 3 space log presuperscript 6 space 2 end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 6 space 6 to the power of begin display style 5 over 2 end style end exponent close parentheses open parentheses log presuperscript 6 space begin display style fraction numerator 3 square root of 2 square root of 3 over denominator 4 end fraction end style close parentheses over denominator 3 space open parentheses log presuperscript 6 space 3 minus log presuperscript 6 space 2 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses begin display style 5 over 2 end style space log presuperscript 6 space 6 close parentheses open parentheses log presuperscript 6 space begin display style fraction numerator 3 times 2 to the power of begin display style 1 half end style end exponent times 3 to the power of begin display style 1 half end style end exponent over denominator 2 squared end fraction end style close parentheses over denominator 3 space open parentheses log presuperscript 6 space 3 minus log presuperscript 6 space 2 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses begin display style 5 over 2 times 1 end style close parentheses open parentheses log presuperscript 6 space begin display style 3 to the power of 1 plus begin display style 1 half end style end exponent over 2 to the power of 2 minus 1 half end exponent end style close parentheses over denominator 3 space open parentheses log presuperscript 6 space 3 minus log presuperscript 6 space 2 close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 5 over 2 end style begin display style space end style open parentheses log presuperscript 6 space begin display style 3 to the power of begin display style 3 over 2 end style end exponent over 2 to the power of 3 over 2 end exponent end style close parentheses over denominator 3 space open parentheses log presuperscript 6 space 3 minus log presuperscript 6 space 2 close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 5 over 2 space open parentheses log presuperscript 6 space 3 to the power of 3 over 2 end exponent minus log presuperscript 6 space 2 to the power of 3 over 2 end exponent close parentheses end style over denominator 3 space open parentheses log presuperscript 6 space 3 minus log presuperscript 6 space 2 close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 5 over 2 space open parentheses 3 over 2 log presuperscript 6 space 3 minus 3 over 2 space log presuperscript 6 space 2 close parentheses end style over denominator 3 space open parentheses log presuperscript 6 space 3 minus log presuperscript 6 space 2 close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 5 over 2 end style times begin display style 3 over 2 end style space up diagonal strike open parentheses log presuperscript 6 space 3 minus log presuperscript 6 space 2 close parentheses end strike over denominator 3 space up diagonal strike open parentheses log presuperscript 6 space 3 minus log presuperscript 6 space 2 close parentheses end strike end fraction end cell row blank equals cell fraction numerator begin display style 15 over 4 end style over denominator 3 end fraction end cell row blank equals cell 15 over 4 divided by 1 third end cell row blank equals cell 15 over 12 end cell row blank equals cell 1 comma 25 end cell end table end style     

Jadi, jawaban yang tepat adalah B.

0

Roboguru

Pembahasan Soal:

Ingat kembali sifat bentuk logaritma berikut ini.

  • log presuperscript a space open parentheses b over c close parentheses equals log presuperscript a space b minus log presuperscript a space c 
  • log presuperscript a space b c equals log presuperscript a space b plus log presuperscript a space c 
  • log presuperscript a space open parentheses b to the power of m close parentheses equals m space open parentheses log presuperscript a space b close parentheses

Dengan sifat  bentuk logaritma di atas, didapat perhitungan berikut ini.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 space log space 0 comma 5 minus log space 225 plus 2 space log space 0 comma 3 plus 6 end cell row blank equals cell 2 space log space open parentheses 5 over 10 close parentheses minus log space 15 squared plus 2 space log space open parentheses 3 over 10 close parentheses plus 6 end cell row blank equals cell 2 space log space 5 minus 2 space log space 10 minus 2 space log space open parentheses 5 times 3 close parentheses plus 2 space log space 3 minus 2 space log space 10 plus 6 end cell row blank equals cell 2 space log space 5 minus 2 space log space 10 minus open parentheses 2 space log space 5 plus 2 space log space 3 close parentheses plus 2 space log space 3 minus 2 space log space 10 plus 6 end cell row blank equals cell up diagonal strike 2 space log space 5 end strike minus 2 space log space 10 minus up diagonal strike 2 space log space 5 end strike minus up diagonal strike 2 space log space 3 end strike plus up diagonal strike 2 space log space 3 end strike minus 2 space log space 10 plus 6 end cell row blank equals cell negative 4 space log space 10 plus 6 end cell row blank equals cell negative 4 times 1 plus 6 end cell row blank equals cell negative 4 plus 6 end cell row blank equals 2 end table end style     

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Bunga majemuk dirumuskan dengan . Nyatakanlah  dalam ,  dan .

Pembahasan Soal:

Ingat kembali sifat bentuk logaritma berikut ini.

  • log presuperscript a space open parentheses b over c close parentheses equals log presuperscript a space b minus log presuperscript a space c 
  • log presuperscript a space b c equals log presuperscript a space b plus log presuperscript a space c 
  • log presuperscript a space open parentheses b to the power of m close parentheses equals m space open parentheses log presuperscript a space b close parentheses 

Dengan sifat  bentuk logaritma di atas, didapat perhitungan berikut ini.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell M subscript n end cell equals cell M open parentheses 1 plus b close parentheses to the power of n end cell row cell log space M subscript n end cell equals cell log space M open parentheses 1 plus b close parentheses to the power of n end cell row cell log space M subscript n end cell equals cell log space M plus log space open parentheses 1 plus b close parentheses to the power of n end cell row cell log space M subscript n minus log space M end cell equals cell log space M plus n space log space open parentheses 1 plus b close parentheses minus log space M end cell row cell fraction numerator log space M subscript n minus log space M over denominator log space open parentheses 1 plus b close parentheses end fraction end cell equals cell fraction numerator n space log space open parentheses 1 plus b close parentheses over denominator log space open parentheses 1 plus b close parentheses end fraction end cell row cell fraction numerator log space M subscript n minus log space M over denominator log space open parentheses 1 plus b close parentheses end fraction end cell equals n row cell fraction numerator log space open parentheses begin display style M subscript n over M end style close parentheses over denominator log space open parentheses 1 plus b close parentheses end fraction end cell equals n end table end style   

Jadi, rumus n yang dinyatakan dalam M subscript nM dan b adalah n equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator log space open parentheses begin display style M subscript n over M end style close parentheses over denominator log space open parentheses 1 plus b close parentheses end fraction end cell end table.

0

Roboguru

Hasil  adalah. . . .

Pembahasan Soal:

Dengan menggunakan sifat bentuk logaritma berikut.

Untuk a comma b comma c greater than 0 dan a not equal to 1, berlaku:

  1. log presuperscript a space a equals 1
  2. log presuperscript a space b to the power of m equals m open parentheses log presuperscript a space b close parentheses
  3. log presuperscript a b over c equals log presuperscript a space b minus log presuperscript a space c
  4. log presuperscript a open parentheses b cross times c close parentheses equals log presuperscript a space b cross times log presuperscript a space c

hasil dari log presuperscript 2 space 18 minus log presuperscript 2 space 8 square root of 2 plus log presuperscript 2 space 1 over 27 minus log presuperscript 2 space 1 third sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell log presuperscript 2 space 18 minus log presuperscript 2 space 8 square root of 2 plus log presuperscript 2 space 1 over 27 minus log presuperscript 2 space 1 third end cell row blank equals cell log presuperscript 2 open parentheses fraction numerator 18 over denominator 8 square root of 2 end fraction close parentheses plus log presuperscript 2 space 1 over 27 minus log presuperscript 2 space 1 third space space space space space space space space space space space space space space Sifat space 3 end cell row blank equals cell log presuperscript 2 open parentheses fraction numerator 18 over denominator 8 square root of 2 end fraction cross times 1 over 27 close parentheses minus log presuperscript 2 space 1 third space space space space space space space space space space space space space space space space space space space space space space Sifat space 4 end cell row blank equals cell log presuperscript 2 open parentheses fraction numerator 18 over denominator 8 square root of 2 end fraction cross times 1 over 27 divided by 1 third 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 Sifat space 3 end cell row blank equals cell log presuperscript 2 open parentheses fraction numerator 18 over denominator 8 square root of 2 end fraction cross times 1 over 27 cross times 3 over 1 close parentheses end cell row blank equals cell log presuperscript 2 open parentheses up diagonal strike 18 to the power of up diagonal strike 2 to the power of 1 end exponent over up diagonal strike 8 square root of 2 end strike to the power of 4 square root of 2 end exponent cross times 1 over up diagonal strike 27 subscript up diagonal strike 9 subscript 1 end subscript cross times up diagonal strike 3 to the power of 1 close parentheses end cell row blank equals cell log presuperscript 2 fraction numerator 1 over denominator 4 square root of 2 end fraction end cell row blank equals cell log presuperscript 2 fraction numerator 1 over denominator 2 squared cross times 2 to the power of begin display style 1 half end style end exponent end fraction end cell row blank equals cell log presuperscript 2 1 over 2 to the power of open parentheses 2 plus begin display style 1 half end style close parentheses end exponent end cell row blank equals cell log presuperscript 2 1 over 2 to the power of begin display style 5 over 2 end style end exponent end cell row blank equals cell log presuperscript 2 space 2 to the power of open parentheses negative 5 over 2 close parentheses end exponent end cell row blank equals cell open parentheses negative 5 over 2 close parentheses cross times 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 Sifat space 2 end cell row blank equals cell open parentheses negative 5 over 2 close parentheses cross times 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 space space space space Sifat space 1 end cell row blank equals cell negative 5 over 2 end cell end table


Hasil dari log presuperscript 2 space 18 minus log presuperscript 2 space 8 square root of 2 plus log presuperscript 2 space 1 over 27 minus log presuperscript 2 space 1 third adalah negative 5 over 2.

Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

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