Question

5*4^x+3*10^x=2*25^x ; найти x

Answer 1

$5* 2^{2x} +3* 2^{x} * 5^{x}=2* 5^{2x} ; 5+3* (frac{5}{2}) ^{x} =2* ( ( frac{5}{2} )^{x} )^{2}; t= ( frac{5}{2} )^{x};$$t textgreater 0, 2 t^{2}-3t-5=0, D=49, t= frac{5}{2}, t=-1 textless 0; ( frac{5}{2} )^{x}= frac{5}{2}; x=1.$