Question

5^x-6*5^-x=3,8 помогите решить

Answer 1

$5^{x}-6cdot 5^{-x}=3,8\\5^{x}-frac{6}{5^{x}}-3,8=0\\t=5^{x} textgreater 0; ,; ; t- frac{6}{t} -3,8=0; |cdot 10\\10t^2-38t-60=0; |:2\\5t^2-19t-30=0\\D=961; ,; ; t_1= frac{19-31}{10}=-1,2 textless 0; ;\\ t_2= frac{19+31}{10} =5\\5^{x}=5quad to quad x=1$