Question

Sa se aduca la forma cea mai simpla expresia.
Bafta INTELIGENŢII

Answer 1

$a)\quad 25^{\log_{5}3} = {(5^2)}^{\log_{5}3} = {(5^{\log_{5}3})}^{2} = 3^2 = 9\\ \\ b)\quad \dfrac{\log_{2}25}{\log_{2}5} = \log_{5}25 = \log_{5}5^2 = 2\log_{5}5=2\\ \\ c)\quad \log_{3}5\cdot \log_4 9\cdot \log_{5}2 = \dfrac{\lg 5}{\lg 3}\cdot \dfrac{\lg 9}{\lg 4}\cdot \dfrac{\lg 2}{\lg 5} = \\ \\ = \dfrac{\lg 5}{\lg 3}\cdot \dfrac{\lg 3^2}{\lg 2^2}\cdot \dfrac{\lg 2}{\lg 5} =\dfrac{\lg 5}{\lg 3}\cdot \dfrac{2\cdot \lg 3}{2\cdot \lg 2}\cdot \dfrac{\lg 2}{\lg 5} =1$