Sagot :
[tex]D:x>0 \wedge x+15>0\\
D:x>0 \wedge x>-15\\
D:x>0\\\\
\log_4x+\log_4(x+15)=2\\
\log_4x(x+15)=2\\
4^2=x(x+15)\\
16=x^2+15x\\
x^2+15x-16=0\\
x^2-x+16x-16=0\\
x(x-1)+16(x-1)=0\\
(x+16)(x-1)=0\\
x=-16 \vee x=1\\
-16\not \in D \Rightarrow \boxed{x=1}[/tex]
Log4(x)+log4(x+15)=2
x>0;
x+15>0 => x>0
Log4(x)+log4(x+15)=2
Log4(x*(x+15))=Log4(16)x*(x+15)=16
x1=1
x2=-16
х=1
x>0;
x+15>0 => x>0
Log4(x)+log4(x+15)=2
Log4(x*(x+15))=Log4(16)x*(x+15)=16
x1=1
x2=-16
х=1