Вычислить: 1) [latex]2^{\frac{log_2 5}{log_5 2}}-5^{log_2 5}[/latex] 2) [latex]3^{2+\frac{log_3 4}{log_4 3}}-9\cdot4^{\frac1{log_43}}+4^{1+log_4 25}[/latex]

1) 2^(log(2)5 / log(5)2) - 5^log(2)5 = = 2^(log(2)5 * log(2)5) - 5^log(2)5 = = (2^log(2)5 )^log(2)5  - 5^log(2)5 = = 5^log(2)5 - 5^log(2)5 = 0 2) 3^( 2 + (log(3)4)/(log(4)3)) - 9*4^(1 / log(4)3) +4^(1 + log(4)25) = = 3^2 * (3^log(3)4)^log(3)4 - 9*4^log(3)4 +4*4^log(4)25 = = 3^2 * 4^log(3)4 - 9 * 4^log(3)4 +4*25 = = 9 * 4^log(3)4 - 9 * 4^log(3)4 +4*25 = 4*25 = 100 [latex]2^{\frac{\log_25}{ \log_52}} - 5^{\log_25} = 2^{\log_25 *\log_25} - 5^{\log_25} =[/latex] [latex]= (2^{\log_25} )^{\log_25} - 5^{\log_25}= 5^{\log_25} - 5^{\log_25} = 0[/latex] [latex]3^{ 2 + \frac{\log_34}{\log_43}} - 9*4^{\frac{1 }{ \log_43}} +4^{1 +\ log_425} = [/latex] [latex]= 3^2 * (3^{\log_34})^{\log_34} - 9*4^{\log_34} +4*4^{\log_425} =[/latex] [latex]= 3^2 * 4^{\log_34} - 9 * 4^{\log_34} +4*25 = \\\\= 9 * 4^{\log_34} - 9 * 4^{\log_34} +4*25 = 4*25 = 100[/latex]

1)  [latex] 2^{ \frac{log_{2}5 }{log_{5}2} } - 5^{log_{2}5} = ( 2^{ log_{2}5} )^{ \frac{1 }{log_{5}2} }- 5^{ \frac{1 }{log_{5}2} }= 5^{ \frac{1 }{log_{5}2} }-5^{ \frac{1 }{log_{5}2} }=0[/latex] 2)  [latex]3^{2+ \frac{log_{3}4 }{log_{4}3} }-9*4^{ \frac{1 }{log_{4}3} } + 4^{1+ log_{4}25} = 3^{2}* (3^{log_{3}4})^{ \frac{1 }{log_{4}3} }-9*4^{ \frac{1 }{log_{4}3}} + \\ +4*4^{log_{4}25}=9*4^{ \frac{1 }{log_{4}3}} - 9*4^{ \frac{1 }{log_{4}3}} +4*25=100 \\ [/latex]