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.$