Question

determinati numarul x care verifica egalitatile. ex. 17 , punctele a, c, e și g.​

Answer 1

Explicație pas cu pas:

3^(x+2)-5*3^x=36 =>

3^x*3²-5*3^x=36 =>

3^x(9-5)=36 => 3^x*4 =36 => 3^x=9 => x=2

5^(x+2)*2^(x+1)+7*10^x=57000 =>

5^x*5²*2^x*2+7*10^x=57000 =>

(5*2)^x*5²*2+7*10^x=57000 =>

10^x*50+7*10^x=57000 =>

10^x*(50+7)=57000 =>

10^x*57=57000 =>

10^x=1000 => x=3

4^(x+2)+4^(x+1)+4^x=336 =>

4^x*4²+4^x*4+4^x=336 =>

4^x*(16+4+1)=336 => 4^x*21=336=>4^x=16 => x=2

7^(x+3)-7^(x+2)-7^(x+1)=41*7^(2x) =>

7^x*7³-7^x*7²-7^x*7=41*7^(2x) =>

7^x*(7³-7²-7)=41*7^(2x) =>

7^x*7*41=41*7^(2x) =>

7^(x+1)=7^(2x) <=> x+1=2x => x=1