Question

মান নির্ণয় কর: $\log_{2\sqrt5}400$

Answer 1

$\log_{2\sqrt5}400$

$=\log_{2\sqrt5}\left(2^4\cdot5^2\right)$

$=\log_{2\sqrt5}\left(2^4\cdot5^{\frac42}\right)$

$=\log_{2\sqrt5}\left(2^4\cdot5^{\frac12\times4}\right)$

$=\log_{2\sqrt5}\left(2\cdot5^{\frac12}\right)^4$

$=\log_{2\sqrt5}\left(2\sqrt5\right)^4$

$=4\log_{2\sqrt5}2\sqrt5$

$=4\times1$

$=4$ [Answer]

Comments

$400$ এর উৎপাদকে বিশ্লেষণ:

$\begin{align}2\left|\underline{400}\right.\\2\left|\underline{200}\right.\\2\left|\underline{100}\right.\\2\left|\underline{50}\right.\\5\left|\underline{25}\right.\\\;\;\;\;\;5\end{align}$
 

$\therefore 400=2\times2\times2\times2\times5\times5=2^4\times5^2$