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Jika 2log5=p dan 3log5=q, nyatakan 30log150 dalam p dan q.

Pertanyaan

Jika 2log5=p dan 3log5=q, nyatakan 30log150 dalam p dan q.

Pembahasan Soal:

Ingat kembali sifat-sifat logaritma:

alog(b×c)alogbaloga===alogb+alogcbloga1,b=11

Diketahui 2log5=p dan 3log5=q maka:

2log53log5==p5log2=p1q5log3=q1 

sehingga

30log150===========30log(30×5)30log30+30log51+5log3011+5log(2×3×5)11+5log2+5log3+5log511+p1+q1+111+pqq+pqp+pqpq11+pqpq+p+q11+pq+p+qpqpq+p+qpq+p+q+pq+p+qpqpq+p+q2pq+p+q 

Dengan demikian bentuk 30log150 dalam p dan q adalah pq+p+q2pq+p+q.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Amamah

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 13 September 2021

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Pertanyaan yang serupa

Jika 2log3=m dan 3log5=n, maka tentukan: b. 2log75

Pembahasan Soal:

Ingat kembali sifat-sifat logaritma berikut:

alogbalogbalogb+alogcalogaalogbm=====plogaplogbbloga1alogbc1malogb   

Diketahui:

2log3=m3log2=m13log5=n 

Maka:

2log75========3log23log753log23log(25×3)m13log25+3log3m13log52+1m123log5+1m12n+1(2n+1)×1m2mn+m 

Jadi, 2log75=2mn+m.

Roboguru

Diketahui log2​5=a dan log3​5=b, maka nilai dari log5​256​ adalah ....

Pembahasan Soal:

Dengan menggunakan sifat-sifat logaritma didapatkan

log5256======log56log525log5(2×3)log552log52+log532log251+log3512a1+b12aba+b2ab

Dengan demikian, log5256=aba+b2ab.

Roboguru

Bentuk sederhana dari

Pembahasan Soal:

Error converting from MathML to accessible text.

Roboguru

Jika diketahui  dan  maka nilai dari  adalah ...

Pembahasan Soal:

Gunakan sifat-sifat logaritma sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a space b end cell equals cell fraction numerator log presuperscript p space b over denominator log presuperscript p space a end fraction end cell row cell log presuperscript a space b end cell equals cell fraction numerator 1 over denominator log presuperscript b space a end fraction end cell row cell log presuperscript a space open parentheses b cross times c close parentheses end cell equals cell log presuperscript a space b plus log presuperscript a space c end cell row cell log presuperscript a space b to the power of m end cell equals cell m times log presuperscript a space b end cell row cell log presuperscript a space a end cell equals 1 end table  

Diketahui undefined maka

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space 3 end cell equals a row cell fraction numerator 1 over denominator log presuperscript 3 space 2 end fraction end cell equals a row cell log presuperscript 3 space 2 end cell equals cell 1 over a end cell end table 

sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log space 21 end scriptbase presuperscript 24 end cell equals cell fraction numerator log presuperscript 3 space 21 over denominator log presuperscript 3 space 24 end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space open parentheses 7 cross times 3 close parentheses over denominator log presuperscript 3 space open parentheses 8 cross times 3 close parentheses end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space 7 plus log presuperscript 3 space 3 over denominator log presuperscript 3 space 8 plus log presuperscript 3 space 3 end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space 7 plus log presuperscript 3 space 3 over denominator log presuperscript 3 space 2 cubed plus log presuperscript 3 space 3 end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space 7 plus log presuperscript 3 space 3 over denominator 3 times log presuperscript 3 space 2 plus log presuperscript 3 space 3 end fraction end cell row blank equals cell fraction numerator b plus 1 over denominator 3 open parentheses begin display style 1 over a end style close parentheses plus 1 end fraction end cell row blank equals cell fraction numerator b plus 1 over denominator begin display style fraction numerator 3 plus a over denominator a end fraction end style end fraction end cell row blank equals cell open parentheses b plus 1 close parentheses cross times fraction numerator a over denominator open parentheses 3 plus a close parentheses end fraction end cell row blank equals cell fraction numerator a plus a b over denominator a plus 3 end fraction end cell end table 

Dengan demikian, nilai dari  begin mathsize 14px style log presuperscript 24 space 21 end style adalah begin mathsize 14px style fraction numerator a plus a b over denominator a plus 3 end fraction end style.

Oleh karena itu, jawaban yang benar adalah C.

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

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