Question

Sa se afle valorile lui x din egalitatile:
a)32 la puterea 25 - 4 la puterea 62 - 8 la puterea 41 = 2 la puterea x ori(x) 4 la puterea x
b)8 la puterea 669 - 4 la puterea 1003 - 32 la puterea 401 = 32 la puterea x
c)16 la puterea 502 - 8 la puterea 669 - 4 la puterea 1003 = 4 la puterea x

Answer 1

a)
2^(5.25)-2^(62.2)-2^(41.3)=2^x.2^2x
2^125-2^124-2^123=2^2x²
2^123(4-2-1)=2^2x²
2^123=2^2x²
123=2x²
x²=123/2
x=+,-√123/2
(asta daca nu ai gresit ceva la redactare)
b)2^(3.669)-2^(2.1003)-2^(5.401)=2^(5x)
2^2007-2^2006-2^2005=2^5x
2^2005(4-2-1)=2^5x
5x=2005
x=401
c)
2^(4.502)-2^(3.669)-2^(2.1003)=2^2x
2^2008-2^2007-2^2006=2^2x
2^2006(4-2-1)=2^2x
2006=2x
x=1003