Pertanyaan

Jika 2 lo g 3 = a dan 3 lo g 5 = b maka 15 lo g 20 = …

Jika $_{2} lo g 3 = a$ dan $_{3} lo g 5 = b$ maka $_{15} lo g 20 = \dots$

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

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Klaim

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Gunakan rumus berikut: Maka

Gunakan rumus berikut:

$begin mathsize 14px style log presubscript presuperscript a invisible function application b equals fraction numerator log presubscript presuperscript c invisible function application b over denominator log presubscript presuperscript c invisible function application a end fraction log presubscript presuperscript a to the power of m end presuperscript invisible function application b to the power of n equals bold n over bold m log presubscript presuperscript a invisible function application b log presubscript presuperscript a invisible function application b equals fraction numerator 1 over denominator log presubscript presuperscript b invisible function application a end fraction log presubscript presuperscript a invisible function application x y equals log presubscript presuperscript a invisible function application x plus log presubscript presuperscript a invisible function application y end style$

Maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript presuperscript 15 invisible function application 20 end cell equals cell fraction numerator log presubscript presuperscript 3 invisible function application 20 over denominator log presubscript presuperscript 3 invisible function application 15 end fraction end cell row blank equals cell fraction numerator log presubscript presuperscript 3 invisible function application open parentheses 2 squared.5 close parentheses over denominator log presubscript presuperscript 3 invisible function application open parentheses 3.5 close parentheses end fraction end cell row blank equals cell fraction numerator 2 log presubscript presuperscript 3 invisible function application 2 plus log presubscript presuperscript 3 invisible function application 5 over denominator log presubscript presuperscript 3 invisible function application 3 plus log presubscript presuperscript 3 invisible function application 5 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 1 over a close parentheses plus b over denominator 1 plus b end fraction end cell row blank equals cell fraction numerator fraction numerator 2 plus a b over denominator a end fraction over denominator 1 plus b end fraction end cell row blank equals cell fraction numerator 2 plus a b over denominator a end fraction cross times fraction numerator 1 over denominator 1 plus b end fraction end cell row blank equals cell fraction numerator 2 plus a b over denominator a open parentheses 1 plus b close parentheses end fraction end cell end table end style$