Question

c14,,c15,c16,c17,c18,c19. Va roog ! urgeent

Answer 1

$14)\log_49=\log_{2^2}3^2=\frac{3}{2}\log_{2^2}3^2=\log_{2^2\cdot2}3^2\cdot3=\log_827$

$15)\log_23\cdot\log_35\cdot\log_58=\frac{\log_{30}3}{\log_{30}2}\cdot\frac{\log_{30}5}{\log_{30}3}\cdot\frac{\log_{30}8}{\log_{30}5}=\frac{\log_{30}8}{\log_{30}2}=\log_28=3$

$16)\log_9\sqrt{3}+\log_4\sqrt{2}=\log_{3^2}3^\frac{1}{2}+\log_{2^2}2^\frac{1}{2}=\frac{2}{2}\log_33+\frac{2}{2}\log_22=\\=1+1=2\in\mathbb{Q}$

$17)\log_2(5+\sqrt{7})+\log_2(5-\sqrt{7})-2\log_23=\log_2((5+\sqrt{7})(5-\sqrt{7}))-\\-\log_23^2=\log_2(25-7)-\log_29=\log_2\frac{18}{9}=\log_22=1\in\mathbb{Z}$

$18)\log_{2\sqrt{2}}3\sqrt{3}=\log_{\sqrt{2^3}}\sqrt{3^3}=\log_{2^{\frac{3}{2}}}{3^{\frac{3}{2}}}=\frac{\frac{3}{2}}{\frac{3}{2}}\log_23=\frac{3}{2}\cdot\frac{2}{3}\log_23=\\=\log_23$

[tex]19)\log_52007 \:\ \textgreater \ \:4\\ \log_52007\:\ \textgreater \ \:\log_55^4\\ 2007\:\ \textgreater \ \:625[/tex]