Question

3*9^х=2*15^х+5*25^х, чему равен х

Answer 1

$3*9^x=2*15^x+5-25^x \ 3*3^{2x}=2*3^x*5^x+5*5^{2x} \ 3^x=u;5^x=v \ 3u^2-2uv-5v^2=0 \ 3*(u/v)^2-2*(u/v)-5=0 \ u/v=t \ 3t^2-2t-5=0 \ t=-1;t=5/3 \ u/v=5/3 \ 5^x/3^x=5/3 \ (5/3)^x=5/3 \ x=1$