Question

Exercitiul 24,punctul a si c.

Answer 1

a)
2^x+2^(x+1)+2^(x+2)+2^(x+3)=240 <=> 2^x+2*2^x+4*2^x+8*2^x=240 <=> 15*2^x=240 <=> 2^x=16 <=> x=4.

c)
S=1+2+2^2+2^3+...+2^x.
2S=2+2^2+2^3+....+2^x+2^(x+1)=(1+2+2^2+2^3+...+2^x)+2^(x+1)-1=S+2^(x+1)-1, deci S=2^(x+1)-1.

Avem deci 2^(x+1)-1=2^75-1 <=> 2^(x+1)=2^75 <=> x+1=75 <=> x=74.