Question

Daca a=2 ( la puterea 123) x 5( la puterea 83 si b=3( la puterea 205) ,atunci mai mic este numarul..

Answer 1

2^(123)=2^(41+41+41) =>2^(41)*2^(41)*2^(41)

5^(83)=5^(41+41+1)=5^(41)*5^(41)*5^(1)

2^(123)*5^(83)=2^(41)*2^(41)*2^(41)*5^(41)*5^(41)*5^(1)=> (2*2*2*5*5)^(41)*5 =>200^(41)*5, deci a=200^(41)*5

3^(205)=3^(5*41)=(3^(5))^(41)=243^(41) , deci b=243^(41)

cum 200^(41)*5<243^(41); rezulta  ca  a<b.