Roboguru

Selesaikan soal berikut! 2. log2+log10−log51​=....

Pertanyaan

Selesaikan soal berikut!

2. log space 2 plus log space 10 minus log space 1 fifth equals.... 

Pembahasan Soal:

Ingat kembali sifat-sifat logaritma berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a space b plus scriptbase log space c end scriptbase presuperscript a end cell equals cell scriptbase log space b c end scriptbase presuperscript a end cell row cell log presuperscript a space b minus l presuperscript a o g space c end cell equals cell l presuperscript a o g space b over c end cell row cell log presuperscript a space a end cell equals 1 end table 

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell log space 2 plus log space 10 minus log space 1 fifth end cell equals cell log space open parentheses fraction numerator 2 cross times 10 over denominator begin display style 1 fifth end style end fraction close parentheses end cell row blank equals cell log space open parentheses 20 cross times 5 over 1 close parentheses end cell row blank equals cell log space 40 end cell row blank equals cell log space open parentheses 10 cross times 4 close parentheses end cell row blank equals cell log space 10 plus log space 4 end cell row blank equals cell 1 plus log space 4 end cell end table 

Jadi, log space 2 plus log space 10 minus log space 1 fifth equals 1 plus log space 4.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

W. Lestari

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 01 September 2021

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Pertanyaan yang serupa

Nilai dari 2log182log26−2log23​=...

Pembahasan Soal:

l presuperscript a o g squared invisible function application b equals to the power of a l o g invisible function application b bullet to the power of a l o g invisible function application b  l presuperscript a o g invisible function application b plus to the power of a l o g invisible function application c equals to the power of a l o g invisible function application left parenthesis b c right parenthesis  l presuperscript a o g invisible function application b minus to the power of a l o g invisible function application c equals to the power of a l o g invisible function application left parenthesis b divided by c right parenthesis  l presuperscript a o g invisible function application a equals 1    M a k a semicolon  fraction numerator left parenthesis squared log squared invisible function application 6 minus squared log squared invisible function application 3 right parenthesis over denominator left parenthesis squared l o g invisible function application 18 right parenthesis end fraction  equals fraction numerator left parenthesis squared log squared invisible function application 6 minus squared log squared invisible function application 3 right parenthesis over denominator left parenthesis squared l o g invisible function application left parenthesis 6 cross times 3 right parenthesis right parenthesis end fraction  equals fraction numerator down diagonal strike left parenthesis squared log invisible function application 6 plus squared log invisible function application 3 right parenthesis end strike left parenthesis squared log invisible function application 6 minus squared log invisible function application 3 right parenthesis over denominator down diagonal strike left parenthesis squared log invisible function application 6 plus squared log invisible function application 3 right parenthesis end strike end fraction  equals squared l o g invisible function application 6 minus squared l o g invisible function application 3  equals squared l o g invisible function application left parenthesis 6 over 3 right parenthesis  equals squared l o g invisible function application left parenthesis 2 right parenthesis  equals 1

0

Roboguru

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

Hasil dari 7log21−7log3+7log35−7log5 adalah...

Pembahasan Soal:

Sifat logaritma :

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a b minus log presuperscript a c end cell equals cell log presuperscript a b over c end cell row cell log presuperscript a b plus log presuperscript a c end cell equals cell log presuperscript a b c end cell row cell log presuperscript a a end cell equals 1 end table

Maka :

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell log presuperscript 7 21 minus log presuperscript 7 3 plus log presuperscript 7 35 minus log presuperscript 7 5 end cell row blank equals cell log presuperscript 7 21 over 3 plus log presuperscript 7 35 over 5 end cell row blank equals cell log presuperscript 7 7 plus log presuperscript 7 7 end cell row blank equals cell 1 plus 1 end cell row blank equals 2 end table

Oleh karena itu, jawaban yang benar adalah D.

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Roboguru

Dengan menggunakan sifat-sifat logaritma tentukan nilai dari: c) 2log16−2⋅2log10+2log25−2log41​

Pembahasan Soal:

Ingat sifat bentuk logatitma berikut.

alogaalogbnalog(bc)alog(cb)====1nalogbalogb+alogcalogbalogc

sehingga dapat ditentukan nilai dari bentuk logaritma berikut. 

n========2log1622log10+2log252log412log162log102+2log252log412log100×4116×252log162log2442log2414  

Dengan demikian, diperoleh hasil dari bentuk logaritma di atas adalah 2log1622log10+2log252log41=4.

0

Roboguru

Nilai dari 5log25+5log3−5log15 = ...

Pembahasan Soal:

i n g a t factorial  to the power of a log space m space plus space to the power of a log space n space equals space to the power of a log left parenthesis m space x space n right parenthesis  to the power of a log space m minus space to the power of a log space n space equals space to the power of a log left parenthesis m over n right parenthesis  to the power of a log space a space equals space 1  M a k a colon  to the power of 5 log space 25 space plus space to the power of 5 log space 3 space minus space to the power of 5 log space 16 space  equals to the power of 5 log space left parenthesis fraction numerator 25 space x space 3 over denominator 15 end fraction right parenthesis  equals to the power of 5 log space 5 space equals space 1

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Roboguru

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