মান নির্ণয় কর: $\log_{2\sqrt5}400$
মান নির্ণয় কর: $\log_{2\sqrt5}400$
1 টি উত্তর পাওয়া গেছে
$\log_{2\sqrt5}400$
$=\log_{2\sqrt5}\left(2^4\cdot5^2\right)$
$=\log_{2\sqrt5}\left(2^4\cdot5^{\frac42}\right)$
$=\log_{2\sqrt5}\left(2^4\cdot5^{\frac12\times4}\right)$
$=\log_{2\sqrt5}\left(2\cdot5^{\frac12}\right)^4$
$=\log_{2\sqrt5}\left(2\sqrt5\right)^4$
$=4\log_{2\sqrt5}2\sqrt5$
$=4\times1$
$=4$ [Answer]
$=\log_{2\sqrt5}\left(2^4\cdot5^2\right)$
$=\log_{2\sqrt5}\left(2^4\cdot5^{\frac42}\right)$
$=\log_{2\sqrt5}\left(2^4\cdot5^{\frac12\times4}\right)$
$=\log_{2\sqrt5}\left(2\cdot5^{\frac12}\right)^4$
$=\log_{2\sqrt5}\left(2\sqrt5\right)^4$
$=4\log_{2\sqrt5}2\sqrt5$
$=4\times1$
$=4$ [Answer]
$\begin{align}2\left|\underline{400}\right.\\2\left|\underline{200}\right.\\2\left|\underline{100}\right.\\2\left|\underline{50}\right.\\5\left|\underline{25}\right.\\\;\;\;\;\;5\end{align}$
$\therefore 400=2\times2\times2\times2\times5\times5=2^4\times5^2$