Pertanyaan

Jika diketahui 2 lo g 5 = a dan 5 lo g 3 = b , maka nilai dari 15 lo g 20 adalah ...

Jika diketahui $^{2} lo g 5 = a$ dan $^{5} lo g 3 = b$ , maka nilai dari $^{15} lo g 20$ adalah ...

$fraction numerator 2 plus a over denominator a left parenthesis b plus 1 right parenthesis end fraction$
$fraction numerator 2 plus a over denominator left parenthesis b plus 1 right parenthesis end fraction$
$fraction numerator 2 plus a over denominator b left parenthesis a plus 1 right parenthesis end fraction$
$fraction numerator 1 plus a over denominator a left parenthesis b plus 2 right parenthesis end fraction$
$fraction numerator 1 plus a over denominator b left parenthesis a plus 2 right parenthesis end fraction$

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M. Mariyam

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Pembahasan

$d e n g a n italic space m e n g g u n a k a n italic space s i f a t italic space l o g a r i t m a l presuperscript italic 2 o g italic space italic 5 italic cross times l presuperscript italic 5 o g italic space italic 3 italic equals a b l presuperscript italic 2 o g italic space italic 3 italic equals a b log presuperscript 15 space 20 equals fraction numerator log presuperscript 2 space 20 over denominator log presuperscript 2 space 15 end fraction equals fraction numerator log presuperscript 2 space left parenthesis 4 cross times 5 right parenthesis over denominator log presuperscript 2 space open parentheses 3 cross times 5 close parentheses end fraction equals fraction numerator log presuperscript 2 space 4 plus log presuperscript 2 space 5 over denominator log presuperscript 2 space 3 plus log presuperscript 2 space 5 end fraction equals fraction numerator log presuperscript 2 space 2 squared plus log presuperscript 2 space 5 over denominator log presuperscript 2 space 3 plus log presuperscript 2 space 5 end fraction equals fraction numerator 2 space. space log presuperscript 2 space 2 space plus log presuperscript 2 space 5 over denominator log presuperscript 2 space 3 plus log presuperscript 2 space 5 end fraction equals fraction numerator 2 space. space 1 space plus a over denominator a b plus a end fraction equals fraction numerator 2 plus a over denominator a left parenthesis b plus 1 right parenthesis end fraction$