Pertanyaan

Jika diketahui 2 lo g 3 = a dan 3 lo g 5 = b . Tentukan 15 lo g 20 ?

Jika diketahui $^{2} lo g 3 = a$ dan $^{3} lo g 5 = b$ . Tentukan $^{15} lo g 20$ ?

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N. Puspita

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Jawaban terverifikasi

Pembahasan

Ingat sifat logaritma berarti = = = = = Jadi = .

Ingat sifat logaritma $begin mathsize 14px style log presuperscript a space b space equals space fraction numerator 1 over denominator log presuperscript b space a end fraction end style$ berarti

$begin mathsize 14px style log presubscript blank presuperscript 3 space 2 space equals space fraction numerator 1 over denominator log presuperscript 2 space 3 end fraction equals 1 over a end style$

begin mathsize 14px style log presuperscript 15 space 20 end style = $begin mathsize 14px style fraction numerator log presuperscript 3 space 20 over denominator log presuperscript 3 space 15 end fraction end style$

= $begin mathsize 14px style fraction numerator log presuperscript 3 space open parentheses 5 cross times 2 cross times 2 close parentheses over denominator log presuperscript 3 space open parentheses 5 cross times 3 close parentheses end fraction end style$

= $begin mathsize 14px style fraction numerator log presuperscript 3 space 5 space plus space 2 cross times log presuperscript 3 space 2 over denominator log presuperscript 3 space 5 space plus space log presuperscript 3 space 3 end fraction end style$

$begin mathsize 14px style equals fraction numerator b plus begin display style 2 over a end style over denominator b plus 1 end fraction end style$

= $begin mathsize 14px style fraction numerator a b plus 2 over denominator a b plus a end fraction end style$

= $begin mathsize 14px style fraction numerator a b plus 2 over denominator a open parentheses b plus 1 close parentheses end fraction end style$

Jadi = $begin mathsize 14px style fraction numerator a b plus 2 over denominator a open parentheses b plus 1 close parentheses end fraction end style$ .