Roboguru

Nilai dari

Pertanyaan

Nilai dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 16 plus log presuperscript 2 4 minus log presuperscript 2 2 end cell equals cell... end cell end table end style 

  1. 2

  2. 3

  3. 4

  4. 5

  5. 6

Pembahasan Soal:

Dengan menggunakkan sifat-sifat logaritma, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px log presuperscript size 14px 2 size 14px 16 size 14px plus size 14px log presuperscript size 14px 2 size 14px 4 size 14px minus size 14px log presuperscript size 14px 2 size 14px 2 end cell size 14px equals cell size 14px log presuperscript size 14px 2 size 14px 2 to the power of size 14px 4 size 14px plus size 14px log presuperscript size 14px 2 size 14px 2 to the power of size 14px 2 size 14px minus size 14px log presuperscript size 14px 2 size 14px 2 end cell row blank size 14px equals cell size 14px 4 size 14px times size 14px log presuperscript size 14px 2 size 14px 2 size 14px plus size 14px 2 size 14px times size 14px log presuperscript size 14px 2 size 14px 2 size 14px minus size 14px log presuperscript size 14px 2 size 14px 2 end cell row blank size 14px equals cell size 14px 4 size 14px times size 14px 1 size 14px plus size 14px 2 size 14px times size 14px 1 size 14px minus size 14px 1 end cell row blank size 14px equals cell size 14px 4 size 14px plus size 14px 2 size 14px minus size 14px 1 end cell row blank size 14px equals size 14px 5 end table 

Oleh karena itu, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

K. Putri

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Terakhir diupdate 29 Maret 2021

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Pertanyaan yang serupa

Nilai dari  adalah

Pembahasan Soal:

Diketahui scriptbase log open parentheses bevelled 1 over 8 close parentheses plus end scriptbase presuperscript 2 scriptbase log open parentheses bevelled 1 over 9 close parentheses plus end scriptbase presuperscript 3 scriptbase log open parentheses bevelled 1 over 125 close parentheses end scriptbase presuperscript 5 comma berdasarkan sifat logaritma scriptbase log open parentheses bevelled 1 over b close parentheses equals negative log presuperscript a open parentheses b close parentheses end scriptbase presuperscript a maka

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log open parentheses bevelled 1 over 8 close parentheses plus end scriptbase presuperscript 2 scriptbase log open parentheses bevelled 1 over 9 close parentheses plus end scriptbase presuperscript 3 scriptbase log open parentheses bevelled 1 over 125 close parentheses end scriptbase presuperscript 5 end cell equals cell negative scriptbase log open parentheses 8 close parentheses minus end scriptbase presuperscript 2 scriptbase log open parentheses 9 close parentheses minus end scriptbase presuperscript 3 scriptbase log open parentheses 125 close parentheses end scriptbase presuperscript 5 end cell row cell scriptbase log open parentheses bevelled 1 over 8 close parentheses plus end scriptbase presuperscript 2 scriptbase log open parentheses bevelled 1 over 9 close parentheses plus end scriptbase presuperscript 3 scriptbase log open parentheses bevelled 1 over 125 close parentheses end scriptbase presuperscript 5 end cell equals cell negative scriptbase log open parentheses 2 cubed close parentheses minus end scriptbase presuperscript 2 scriptbase log open parentheses 3 squared close parentheses minus end scriptbase presuperscript 3 scriptbase log open parentheses 5 cubed close parentheses end scriptbase presuperscript 5 end cell end table


Berdasarkan sifat logaritma scriptbase log open parentheses b to the power of m close parentheses equals m cross times log presuperscript a open parentheses b close parentheses end scriptbase presuperscript a dan log presuperscript a open parentheses a close parentheses equals 1 maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log open parentheses bevelled 1 over 8 close parentheses plus end scriptbase presuperscript 2 scriptbase log open parentheses bevelled 1 over 9 close parentheses plus end scriptbase presuperscript 3 scriptbase log open parentheses bevelled 1 over 125 close parentheses end scriptbase presuperscript 5 end cell equals cell negative scriptbase log open parentheses 2 cubed close parentheses minus end scriptbase presuperscript 2 scriptbase log open parentheses 3 squared close parentheses minus end scriptbase presuperscript 3 scriptbase log open parentheses 5 cubed close parentheses end scriptbase presuperscript 5 end cell row cell scriptbase log open parentheses bevelled 1 over 8 close parentheses plus end scriptbase presuperscript 2 scriptbase log open parentheses bevelled 1 over 9 close parentheses plus end scriptbase presuperscript 3 scriptbase log open parentheses bevelled 1 over 125 close parentheses end scriptbase presuperscript 5 end cell equals cell negative 3 cross times scriptbase log open parentheses 2 close parentheses minus 2 cross times end scriptbase presuperscript 2 scriptbase log open parentheses 3 close parentheses minus end scriptbase presuperscript 3 3 cross times scriptbase log open parentheses 5 close parentheses end scriptbase presuperscript 5 end cell row cell scriptbase log open parentheses bevelled 1 over 8 close parentheses plus end scriptbase presuperscript 2 scriptbase log open parentheses bevelled 1 over 9 close parentheses plus end scriptbase presuperscript 3 scriptbase log open parentheses bevelled 1 over 125 close parentheses end scriptbase presuperscript 5 end cell equals cell negative 3 cross times 1 negative 2 cross times 1 minus 3 cross times 1 end cell row cell scriptbase log open parentheses bevelled 1 over 8 close parentheses plus end scriptbase presuperscript 2 scriptbase log open parentheses bevelled 1 over 9 close parentheses plus end scriptbase presuperscript 3 scriptbase log open parentheses bevelled 1 over 125 close parentheses end scriptbase presuperscript 5 end cell equals cell negative 3 minus 2 minus 3 end cell row cell scriptbase log open parentheses bevelled 1 over 8 close parentheses plus end scriptbase presuperscript 2 scriptbase log open parentheses bevelled 1 over 9 close parentheses plus end scriptbase presuperscript 3 scriptbase log open parentheses bevelled 1 over 125 close parentheses end scriptbase presuperscript 5 end cell equals cell negative 8 end cell end table


Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

Hitunglah

Pembahasan Soal:

Logaritma adalah suatu operasi invers atau kebalikan dari perpangkatan.

Terdapat dua sifat logaritma yang digunakan dalam proses penyelesaian, yaitu:

begin mathsize 14px style log presuperscript a space a equals 1 log presuperscript a space b to the power of m equals m times log presuperscript a space b end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 3 1 over 9 square root of 3 end cell equals cell log presuperscript 3 square root of 1 over 9 squared cross times 3 end root end cell row blank equals cell log presuperscript 3 square root of 1 over 3 to the power of 4 cross times 3 end root end cell row blank equals cell log presuperscript 3 square root of 3 to the power of negative 4 end exponent cross times 3 end root end cell row blank equals cell log presuperscript 3 square root of 3 to the power of negative 3 end exponent end root end cell row blank equals cell log presuperscript 3 space open parentheses 3 to the power of negative 3 end exponent close parentheses to the power of begin inline style 1 half end style end exponent end cell row blank equals cell log presuperscript 3 space 3 to the power of negative begin inline style 3 over 2 end style end exponent end cell row blank equals cell negative 3 over 2 cross times log presuperscript 3 space 3 end cell row blank equals cell negative 3 over 2 end cell end table end style 

Jadi, nilai begin mathsize 14px style log presuperscript 3 1 over 9 square root of 3 equals negative 3 over 2 end style.

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Roboguru

Bentuk sederhana dari

Pembahasan Soal:

fraction numerator log presubscript space presuperscript 2 invisible function application 16 over 9 plus fraction numerator 1 over denominator log presubscript space presuperscript 18 invisible function application 2 end fraction minus log presubscript space presuperscript 7 invisible function application 7 over denominator log presubscript space presuperscript 3 invisible function application 4. log presubscript space presuperscript 4 invisible function application 6. log presubscript space presuperscript 6 invisible function application 9 end fraction equals fraction numerator log presubscript space presuperscript 2 invisible function application 16 over 9 plus log presubscript space presuperscript 2 invisible function application 18 minus 1 over denominator log presubscript space presuperscript 3 invisible function application 9 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 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 presubscript space presuperscript 2 invisible function application open parentheses 16 over 9 cross times 18 close parentheses space minus 1 over denominator log presubscript space presuperscript 3 invisible function application 9 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 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 presubscript space presuperscript 2 invisible function application 32 space minus 1 over denominator log presubscript space presuperscript 3 invisible function application 3 squared 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 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 presubscript space presuperscript 2 invisible function application 2 to the power of 5 space minus 1 over denominator 2. log presubscript space presuperscript 3 invisible function application 3 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 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 5. log presubscript space presuperscript 2 invisible function application 2 minus 1 over denominator 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 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

Pembahasan Soal:

table row 9 row space end table log invisible function application 150 equals fraction numerator table row 2 row space end table log invisible function application space 150 over denominator table row 2 row space end table log invisible function application space 9 end fraction equals fraction numerator table row 2 row space end table log invisible function application space left parenthesis 2 cross times 3 cross times 5 squared right parenthesis over denominator table row 2 row space end table log invisible function application space 3 squared end fraction equals fraction numerator table row 2 row space end table log invisible function application space open parentheses 2 close parentheses plus table row 2 row space end table log invisible function application space 3 plus table row 2 row space end table log invisible function application space 5 squared over denominator 2 times table row 2 row space end table log invisible function application space 3 end fraction equals fraction numerator table row 2 row space end table log invisible function application space open parentheses 2 close parentheses plus table row 2 row space end table log invisible function application space 3 plus 2 times table row 2 row space end table log invisible function application space 5 over denominator 2 times table row 2 row space end table log invisible function application space 3 end fraction equals fraction numerator 1 invisible function application space plus a plus 2 b over denominator 2 a end fraction

0

Roboguru

Nilai dari

Pembahasan Soal:

log presubscript space presuperscript 2 superscript space invisible function application left parenthesis 8 cross times 16 right parenthesis equals log presubscript space presuperscript 2 superscript space invisible function application left parenthesis 2 cubed cross times 2 to the power of 4 right parenthesis  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 2 superscript space invisible function application left parenthesis 2 to the power of 7 right parenthesis  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 7. space log presubscript space presuperscript 2 superscript space invisible function application 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 equals 7

0

Roboguru

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