Question

Dapatkah anda menyelesaikan nya? Berapa nilai dari
[tex]\displaystyle\frac{\log 32~\log 49}{\log 343~\log 128}[/tex]

Answer 1

Sifat logaritma:

[tex]^alog({b^{n}})=n\times^alog_b[/tex]

[tex]\frac{log(32)\times log(49)}{log(343)\times log(128)} =\frac{log(2^5)\times log(7^2)}{log(7^3)\times log(2^7)}[/tex]

[tex]\frac{log(2^5)\times log(7^2)}{log(7^3)\times log(2^7)}=\frac{5\times log(2)\times2\times log(7)}{3\times log(7)\times7\times log(2)}[/tex]

Coret log(2) dan log(7):

[tex]\frac{5\times log(2)\times2\times log(7)}{3\times log(7)\times7\times log(2)}=\frac{5\times2}{3\times7}=\frac{10}{21}[/tex]

Answer 2

Verified answer

Jawab:
[tex]\displaystyle=\frac{10}{21}[/tex]

Penjelasan dengan langkah-langkah:
[tex]\displaystyle\frac{log32\:\:log49}{log343\:\:log128}=\frac{log32}{log343}\cdot\frac{log49}{log128}\\\\=\frac{log(2^5)}{log(7^3)}\cdot\frac{log(7^2)}{log(2^7)}\:\:\because\:log_a(b^c)=c\cdot log_a(b)\:\therefore\\\\=\frac{5\not log2}{3\not log7}\cdot\frac{2\not log7}{7\not log2}\\\\=\frac{10}{21}[/tex]

(xcvi)