Question

resolva as equações:

a) log4x+ log2x=6
b) logx(2x+3)=2

Answer 1

$Ola'! \\ \\ a) \\ log_{4}x+log_{2}x=6 \\ \\ \frac{log_{2}x}{log_{2}4}+log_{2}x=6 \\ \\ log_{2}x+2log_{2}x=12 \\ \\ log_{2}x=4 \\ \\ \boxed{\boxed{x=16}} \\ \\ ====================================== \\ b) \\ log_{x}(2x+3)=2 \\ \\ x^{2} =2x+3 \\ \\ x^{2} -2x-3=0 \\ \\ x_1=3 \\ x_2=-1 \\ \\ Ent\~ao~a ~a~resposta ~e': \boxed{\boxed{x=3}}$