Pertanyaan

Hasil dari adalah ...

Hasil dari $fraction numerator log subscript 5 space square root of 32 times log subscript 2 space 9 times log subscript 3 space begin display style 1 over 25 end style over denominator log subscript square root of 2 end subscript space 28 minus log subscript square root of 2 end subscript space 7 end fraction$ adalah ... $\;$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat! a lo g a a lo g b ⋅ b lo g c a m lo g b n a lo g b − a lo g c = = = = 1 a lo g c m n a lo g b a lo g c b Maka, hasil dari adalah: Sehingga, . Jadi, jawaban yang tepat adalah C.

Ingat!

$^{a} lo g a^{a} lo g b \cdot^{b} lo g c^{a^{m}} lo g b^{n}^{a} lo g b -^{a} lo g c = = = = 1^{a} lo g c \frac{n}{m}^{a} lo g b^{a} lo g \frac{b}{c}$

Maka, hasil dari $fraction numerator scriptbase log space square root of 32 end scriptbase presuperscript 5 times scriptbase log space 9 end scriptbase presuperscript 2 times scriptbase log space begin display style 1 over 25 end style space end scriptbase presuperscript 3 over denominator scriptbase log space 28 end scriptbase presuperscript square root of 2 end presuperscript minus scriptbase log space 7 end scriptbase presuperscript square root of 2 end presuperscript end fraction$ adalah:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator scriptbase log space square root of 32 end scriptbase presuperscript 5 times scriptbase log space 9 end scriptbase presuperscript 2 times scriptbase log space begin display style 1 over 25 end style space end scriptbase presuperscript 3 over denominator scriptbase log space 28 end scriptbase presuperscript square root of 2 end presuperscript minus scriptbase log space 7 end scriptbase presuperscript square root of 2 end presuperscript end fraction end cell row blank equals cell fraction numerator scriptbase log space square root of 2 to the power of 5 end root end scriptbase presuperscript 5 times scriptbase log space 3 squared end scriptbase presuperscript 2 times scriptbase log space begin display style 1 over 5 squared end style space end scriptbase presuperscript 3 over denominator scriptbase log space 28 end scriptbase presuperscript square root of 2 end presuperscript minus scriptbase log space 7 end scriptbase presuperscript square root of 2 end presuperscript end fraction end cell row blank equals cell fraction numerator scriptbase log space 2 to the power of begin display style 5 over 2 end style end exponent end scriptbase presuperscript 5 times scriptbase log space 3 squared end scriptbase presuperscript 2 times scriptbase log space begin display style 5 to the power of negative 2 end exponent end style space end scriptbase presuperscript 3 over denominator scriptbase log space 28 end scriptbase presuperscript 2 to the power of begin display style 1 half end style end exponent end presuperscript minus scriptbase log space 7 end scriptbase presuperscript blank presuperscript 2 to the power of 1 half end exponent end presuperscript end presuperscript end fraction end cell row blank equals cell fraction numerator 5 over 2 times scriptbase log space 2 end scriptbase presuperscript 5 times 2 times scriptbase log space 3 end scriptbase presuperscript 2 times open parentheses negative 2 close parentheses times scriptbase log space begin display style 5 end style space end scriptbase presuperscript 3 over denominator scriptbase log space begin display style 28 over 7 end style end scriptbase presuperscript 2 to the power of begin display style 1 half end style end exponent end presuperscript end fraction end cell row blank equals cell fraction numerator 5 over 2 times 2 times open parentheses negative 2 close parentheses scriptbase log space 2 end scriptbase presuperscript 5 times scriptbase log space 3 end scriptbase presuperscript 2 times scriptbase log space begin display style 5 end style space end scriptbase presuperscript 3 over denominator scriptbase log space begin display style 4 end style end scriptbase presuperscript 2 to the power of begin display style 1 half end style end exponent end presuperscript end fraction end cell row blank equals cell fraction numerator open parentheses negative 10 close parentheses scriptbase log space begin display style 5 end style space end scriptbase presuperscript 5 over denominator scriptbase log space 2 squared end scriptbase presuperscript 2 to the power of begin display style 1 half end style end exponent end presuperscript end fraction end cell row blank equals cell fraction numerator open parentheses negative 10 close parentheses times 1 over denominator 4 times scriptbase log space 2 space end scriptbase presuperscript 2 end fraction end cell row blank equals cell fraction numerator negative 10 over denominator 4 times 1 end fraction end cell row blank equals cell negative 10 over 4 end cell row blank equals cell negative 5 over 2 end cell end table$

Sehingga, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator scriptbase log space square root of 32 end scriptbase presuperscript 5 times scriptbase log space 9 end scriptbase presuperscript 2 times scriptbase log space begin display style 1 over 25 end style space end scriptbase presuperscript 3 over denominator scriptbase log space 28 end scriptbase presuperscript square root of 2 end presuperscript minus scriptbase log space 7 end scriptbase presuperscript square root of 2 end presuperscript end fraction end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 2 end cell end table$ .

Jadi, jawaban yang tepat adalah C.