Diketahui 2log 5=b dan 5log 3=c, maka nilai dari8log (5+26−5−26)=...

Pertanyaan

Diketahui ${}^2\log\;5=b\;\mathrm{dan}\;\;^5\log\;3=c$ , maka nilai dari ${}^8\log\;\left(\sqrt{5+2\sqrt6}-\sqrt{5-2\sqrt6}\right)=...$

$\frac12$
$\frac13$
$\frac14$
$\frac15$
$\frac16$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Ingat

${}^{a^m}\log\;b^n=\frac mn\cdot^a\log\;b$
$\sqrt{\left(a+b\right)\pm2\sqrt{ab}}=\sqrt a\pm\sqrt b$

Perhatikan perhitungan berikut

$blank to the power of 8 log space open parentheses square root of 5 plus 2 square root of 6 end root minus square root of 5 minus 2 square root of 6 end root close parentheses equals to the power of 8 log space open parentheses square root of open parentheses 3 plus 2 close parentheses plus 2 square root of 3 cross times 2 end root end root minus square root of open parentheses 3 plus 2 close parentheses minus 2 square root of 3 cross times 2 end root end root close parentheses equals to the power of 8 log space open square brackets open parentheses square root of 3 plus square root of 2 close parentheses minus open parentheses square root of 3 minus square root of 2 close parentheses close square brackets equals to the power of 8 log space open parentheses square root of 3 plus square root of 2 minus square root of 3 plus square root of 2 close parentheses equals to the power of 8 log space open parentheses 2 square root of 2 close parentheses equals to the power of 2 cubed end exponent log space 2 to the power of 3 over 2 end exponent equals fraction numerator begin display style 3 over 2 end style over denominator 3 end fraction times squared log space 2 equals 1 half times 1 equals 1 half$

Oleh karena itu, jawaban yang benar adalah A.