Pertanyaan

Nilai adalah ...

Nilai ${}^\sqrt2{\log\;8-{}^2{\log\;{\textstyle\frac12}\sqrt2}}$ adalah ...

$6 \frac{1}{2}$
$5 \frac{1}{2}$
$4 \frac{1}{2}$
$3 \frac{1}{2}$
$2 \frac{1}{2}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Ingat sifat logaritma: a m lo g ( b n ) = m n ⋅ a lo g ( b ) a lo g ( b ⋅ c ) = a lo g ( b ) + a lo g ( c ) Sehingga: Oleh karena itu, jawaban yang benar adalah A.

Ingat sifat logaritma:

$^{a^{m}} lo g (b^{n}) = \frac{n}{m} \cdot^{a} lo g (b)$
$^{a} lo g (b \cdot c) =^{a} lo g (b) +^{a} lo g (c)$

Sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell scriptbase log open parentheses 8 close parentheses minus scriptbase log open parentheses begin inline style bevelled 1 half end style square root of 2 close parentheses end scriptbase presuperscript 2 end scriptbase presuperscript square root of 2 end presuperscript end cell row blank equals cell scriptbase log open parentheses 2 cubed close parentheses end scriptbase presuperscript 2 to the power of 1 half end exponent end presuperscript minus open parentheses scriptbase log open parentheses 2 to the power of negative 1 end exponent close parentheses end scriptbase presuperscript 2 plus scriptbase log open parentheses 2 to the power of begin inline style bevelled 1 half end style end exponent close parentheses end scriptbase presuperscript 2 close parentheses end cell row blank equals cell fraction numerator 3 over denominator bevelled 1 half end fraction times scriptbase log open parentheses 2 close parentheses end scriptbase presuperscript 2 minus open parentheses open parentheses negative 1 close parentheses times scriptbase log open parentheses 2 close parentheses end scriptbase presuperscript 2 plus 1 half times scriptbase log open parentheses 2 close parentheses end scriptbase presuperscript 2 close parentheses end cell row blank equals cell 6 cross times 1 minus open parentheses open parentheses negative 1 close parentheses cross times 1 plus 1 half cross times 1 close parentheses end cell row blank equals cell 6 minus open parentheses negative 1 plus 1 half close parentheses end cell row blank equals cell 6 minus open parentheses negative 1 half close parentheses end cell row blank equals cell 6 plus 1 half end cell row blank equals cell 6 1 half end cell end table$

Oleh karena itu, jawaban yang benar adalah A.