1) Rozwiąż równanie: [latex]5^x^+^{2}-5^x=120[/latex]   2)Oblicz: [latex]27^frac{2}{3}*9=x [/latex] [latex]2^x^-^1=8[/latex]   3)Oblicz: [latex]log_frac{1}{2}8[/latex] [latex]log_2x=-3[/latex] [latex]log_327 - log_31[/latex]

1) [latex]5^{x+2}-5^{x}=120[/latex] [latex]5^{x}(5^2-1)=120[/latex] [latex]5^{x} cdot 24=120[/latex] |:24 [latex]5^{x}=5[/latex] [latex]x=1[/latex] 2) [latex]27^{frac{2}{3}} cdot 9=x[/latex] [latex](sqrt[3]{27})^2 cdot 9=x[/latex] [latex]3^2 cdot 9=x[/latex] [latex]x=81[/latex] [latex]2^{x-1}=8[/latex] [latex]2^{x-1}=2^3[/latex] [latex]x-1=3[/latex] [latex]x=4[/latex] 3) [latex]log_{frac{1}{2}}8=c[/latex] [latex](frac{1}{2})^c=8[/latex] [latex]2^{-c}=8[/latex] [latex]-c=3[/latex] [latex]c=-3[/latex] [latex]log_{2}x=-3[/latex] [latex]2^{-3}=x[/latex] [latex](frac{1}{2})^3=x[/latex] [latex]x=frac{1}{8}[/latex] [latex]log_{3}27-log_{3}1=log_{3} frac{27}{1}=log_{3}27=3[/latex]