Question

দেখাও যে, $\log_{10}\frac{50}{147}=\log_{10}2+\log_{10}5-\log_{10}3-2\log_{10}7$

Answer 1

Left Hand Side,
$\log_{10}\frac{50}{147}$

$=\log_{10}50-\log_{10}147$

$=\log_{10}\left(2\times5\times5\right)-\log_{10}\left(3\times7\times7\right)$

$=\left(\log_{10}2+\log_{10}5^2\right)-\left(\log_{10}3+\log_{10}7^2\right)$

$=\log_{10}2+\log_{10}5^2-\log_{10}3-\log_{10}7^2$

$=\log_{10}2+2\log_{10}5-\log_{10}3-2\log_{10}7$

$=$ Right Hand Side [Showed]