Pertanyaan

Jika ab lo g a = 4 , maka ab lo g b 3 a = ....

Jika $_{ab} lo g a = 4, maka_{ab} lo g \frac{3 a}{b} =$ ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Perhatikan bahwa Kita cari nilai dari . Diketahui .Perhatikan bahwa Jadi, Dengan demikian, jawaban yang tepat adalah E.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript blank presuperscript ab invisible function application fraction numerator cube root of straight a over denominator square root of straight b end fraction end cell equals cell log presubscript blank presuperscript ab invisible function application cube root of straight a minus log presubscript blank presuperscript ab invisible function application square root of straight b end cell row blank equals cell log presubscript blank presuperscript ab invisible function application straight a to the power of 1 third end exponent minus log presubscript blank presuperscript ab invisible function application straight b to the power of 1 half end exponent end cell row blank equals cell 1 third log presubscript blank presuperscript ab invisible function application straight a minus 1 half log presubscript blank presuperscript ab invisible function application straight b end cell row blank equals cell 1 third left parenthesis 4 right parenthesis minus 1 half open parentheses fraction numerator 1 over denominator log presubscript blank presuperscript straight b invisible function application ab end fraction close parentheses end cell row blank equals cell 4 over 3 minus 1 half open parentheses fraction numerator 1 over denominator log presubscript blank presuperscript straight b invisible function application straight a plus log presubscript blank presuperscript straight b invisible function application straight b end fraction close parentheses end cell row blank equals cell 4 over 3 minus 1 half open parentheses fraction numerator 1 over denominator log presubscript blank presuperscript straight b invisible function application straight a plus 1 end fraction close parentheses end cell end table end style$

Kita cari nilai dari .

Diketahui . Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript blank presuperscript ab invisible function application straight a end cell equals 4 row cell fraction numerator 1 over denominator log presubscript blank presuperscript straight a invisible function application ab end fraction end cell equals 4 row cell fraction numerator 1 over denominator log presubscript blank presuperscript straight a invisible function application straight a plus log presubscript blank presuperscript straight a invisible function application straight b end fraction end cell equals 4 row cell fraction numerator 1 over denominator 1 plus log presubscript blank presuperscript straight a invisible function application straight b end fraction end cell equals 4 row cell 1 plus log presubscript blank presuperscript straight a invisible function application straight b end cell equals cell 1 fourth end cell row cell log presubscript blank presuperscript straight a invisible function application straight b end cell equals cell 1 fourth minus 1 end cell row cell log presubscript blank presuperscript straight a invisible function application straight b end cell equals cell negative 3 over 4 end cell row cell log presubscript blank presuperscript straight b invisible function application straight a end cell equals cell negative 4 over 3 end cell end table end style$

Jadi,

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Dengan demikian, jawaban yang tepat adalah E.