5^x-5^(x-1)=100 9^(x+1)+3^(2x+4)=30 решите с - вопрос №34570585511009132430 от mariyakarimova2 30.07.2022 23:14

Question

Алгебра: 5^x-5^(x-1)=100 9^(x+1)+3^(2x+4)=30 решите с пояснением!

mariyakarimova2 · Answer

5 ^ X - 5 ^ ( X - 1 ) = 100
5 ^ X * ( 1 - ( 1/5 )) = 100
5 ^ X = 100 : ( 4/5 )
5 ^ X = 125
5 ^ X = 5 ^ 3
X = 3

9 ^ ( X+ 1 ) + 3 ^ ( 2X + 4 ) = 30
( 3 ^ 2 ) ^ ( X + 1 ) + 3 ^ ( 2X + 4 ) = 30
3 ^ ( 2X + 2 ) + 3 ^ ( 2X + 4 ) = 30
3 ^ 2X * ( 3 ^2 + 3^4 ) = 30
3 ^ 2X = 30 : ( 9 + 81 )
3 ^ 2X = 30 : 90
3 ^ 2X = ( 1/3 )
3 ^ 2X = 3 ^ - 1
2X = - 1
X = - 0,5