Proszę o pomoc!! 1.Rozwiąż równanie a)[latex] 5^{2x} -3*5^x-10=0 [/latex] b) [latex]7*7^2^x-8*7^x+1=0[/latex] c)[latex]4^x-5*2^x+4=0[/latex] d)[latex]4^x-6*2^x-16=0[/latex] e)[latex]9^x-25*3^x-54=0[/latex] f)[latex]5*25^x+49*5^x-10=0[/latex]

[latex]a)5^{2x}-3cdot 5^x-10=0 \niech quad 5^x=t, ; t>0 \t^2-3t-10=0 \Delta=9+40=49 \sqrt{Delta}=7 \t_1=frac{3-7}{2}=-2<0 \t_2=frac{3+7}{2}=5 \\5^x=5 \oxed{x=1}[/latex] ==================== [latex]b)7cdot 7^{2x}-8cdot 7^x+1=0 \niech quad 7^x=t,;t>0 \7t^2-8t+1=0 \Delta=64-28=36 \sqrt{Delta}=6 \t_1=frac{8-6}{14}=frac{1}{7} \t_2=frac{8+6}{14}=1 \\7^x=frac{1}{7} quadvee quad7^x=1 \oxed{x=-1 quad vee quad x=0}[/latex] =================== [latex]c)4^x-5cdot2^x+4=0 \2^{2x}-5cdot2^x+4=0 \niech quad 2^x=t,; t>0 \t^2-5t+4=0 \Delta=25-16=9 \sqrt{Delta}=3 \t_1=frac{5-3}{2}=1 \t_2=frac{5+3}{2}=4 \\2^x=1quad vee quad 2^x=4 \oxed{x=0 quad vee quad x=2}[/latex] =================== [latex]d)4^x-6cdot 2^x-16=0 \2^{2x}-6cdot 2^x-16=0 \niech quad 2^x=t, ; t>0 \t^2-6t-16=0 \Delta=36+64=100 \sqrt{Delta}=10 \t_1=frac{6-10}{2}=-2<0 \t_2=frac{6+10}{2}=8 \\2^x=8 \oxed{x=3}[/latex] ==================== [latex]e)9^x-25cdot 3^x-54=0 \3^{2x}-25cdot 3^x-54=0 \niech quad 3^x=t,;t>0 \t^2-25t-54=0 \Delta=625+216=841 \sqrt{Delta}=29 \t_1=frac{25-29}{2}=-2<0 \t_2=frac{25+29}{2}=27 \\3^x=27 \oxed{x=3}[/latex] ==================== [latex]f)5cdot 25^x+49cdot 5^x-10=0 \5cdot 5^{2x}+49cdot 5^x-10=0 \niech quad 5^x=t,;t>0 \5t^2+49t-10=0 \Delta=2401+200=2601 \sqrt{Delta}=51 \t_1=frac{-49-51}{10}=-10<0 \t_2=frac{-49+51}{10}=frac{1}{5} \\5^x=frac{1}{5} \oxed{x=-1}[/latex]