Pertanyaan

Jika 2 lo g 3 = p dan 3 lo g 7 = q , maka 21 lo g 54 = …

Jika $^{2} lo g 3 = p$ dan $^{3} lo g 7 = q$ , maka $^{21} lo g 54 = \dots$

$fraction numerator p plus 3 over denominator p q end fraction$
$fraction numerator 3 p plus 3 over denominator p q plus p end fraction$
$fraction numerator 3 p plus 3 over denominator p q minus p end fraction$
$fraction numerator 3 p plus 1 over denominator p q plus p end fraction$
$fraction numerator 3 p plus 1 over denominator p q minus p end fraction$

W. Wati

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D

Pembahasan

Ingat sifat-sifat logaritma berikut: Berdasarkan sifat-sifat logaritma di atas, diperoleh perhitungansebagai berikut: Oleh karena itu, jawaban yang tepat adalah D

Ingat sifat-sifat logaritma berikut:

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

Berdasarkan sifat-sifat logaritma di atas, diperoleh perhitungan sebagai berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 21 space 54 end cell equals cell fraction numerator log presuperscript 3 space 54 over denominator log presuperscript 3 space 21 end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space open parentheses 27 cross times 2 close parentheses over denominator log presuperscript 3 space open parentheses 3 cross times 7 close parentheses end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space 27 plus log presuperscript 3 space 2 over denominator log presuperscript 3 space 3 plus log presuperscript 3 space 7 end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space 3 cubed plus log presuperscript 3 space 2 over denominator log presuperscript 3 space 3 plus log presuperscript 3 space 7 end fraction end cell row blank equals cell fraction numerator open parentheses 3 cross times log presuperscript 3 space 3 close parentheses plus log presuperscript 3 space 2 over denominator log presuperscript 3 space 3 plus log presuperscript 3 space 7 end fraction end cell row blank equals cell fraction numerator 3 plus begin display style 1 over p end style over denominator 1 plus q end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 3 p plus 1 over denominator p end fraction end style over denominator 1 plus q end fraction end cell row blank equals cell fraction numerator 3 p plus 1 over denominator p end fraction cross times fraction numerator 1 over denominator 1 plus q end fraction end cell row blank equals cell fraction numerator 3 p plus 1 over denominator p plus p q end fraction end cell end table$

Oleh karena itu, jawaban yang tepat adalah D