Question

Comparati nr a=5x5^2x5^3x........x5^50   si b =2^3825

Answer 1

[tex]a=5*5^2*5^3*....*5^{50} \\ \\ a=5^{(1+2+3+...+50)} \\ \\ a= 5^{ \frac{50(50+1)}{2}} \\ \\ a=5^{25*51} \\ \\ a=5^{1275} \\ \\ b=2^{3825} \\ \\ a=5^{3*425}~si~b=2^{9*425} \\ \\ a=(5^3)^{425}~si~ b=(2^9)^{425} \\ \\ a=125^{425}~si~b=512^{425} => \\ \\ =>a<b[/tex]