Đáp án:
$10) \left[\begin{array}{l} x=0\\ x=1\end{array} \right.\\ 11) \left[\begin{array}{l} x=0\\ x=1\end{array} \right.\\ 12) \left[\begin{array}{l} x=\dfrac{\log_62}{1-\log_65}\\ x=0\end{array} \right.\\ 13) x=0$
Giải thích các bước giải:
$10)\\ 5^x-6+5^{1-x}=0\\ \Leftrightarrow 5^x(5^x-6+5^{1-x})=0.5^x\\ \Leftrightarrow (5^x)^2-6.5^x+5=0\\ \Leftrightarrow (5^x)^2-5.5^x-5^x+5=0\\ \Leftrightarrow 5^x(5^x-5)-(5^x+5)=0\\ \Leftrightarrow (5^x-1)(5^x-5)=0\\ \Leftrightarrow \left[\begin{array}{l} 5^x-1=0\\ 5^x-5=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} 5^x=1\\ 5^x=5\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=0\\ x=1\end{array} \right.\\ 11)\\ 25^x-6.5^x+5=0\\ \Leftrightarrow (5^2)^x-6.5^x+5=0\\ \Leftrightarrow 5^{2x}-6.5^x+5=0\\ \Leftrightarrow (5^x)^2-6.5^x+5=0\\ \Leftrightarrow (5^x)^2-5.5^x-5^x+5=0\\ \Leftrightarrow 5^x(5^x-5)-(5^x+5)=0\\ \Leftrightarrow (5^x-1)(5^x-5)=0\\ \Leftrightarrow \left[\begin{array}{l} 5^x-1=0\\ 5^x-5=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} 5^x=1\\ 5^x=5\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=0\\ x=1\end{array} \right.\\ 12)\\ 36^x-3.30^x+2.25^x=0\\ \Leftrightarrow (6^2)^x-3.(6.5)^x+2.(5^2)^x=0\\ \Leftrightarrow 6^{2x}-3.6^x.5^x+2.5^{2x}=0\\ \Leftrightarrow (6^x)^2-6^x.5^x-2.6^x.5^x+2.(5^x)^2=0\\ \Leftrightarrow 6^x(6^x-5^x)-2.5^x(6^x-5^x)=0\\ \Leftrightarrow (6^x-2.5^x)(6^x-5^x)=0\\ \Leftrightarrow \left[\begin{array}{l} 6^x-2.5^x=0\\ 6^x-5^x=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} 6^x=2.5^x\\ 6^x=5^x\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} \log_66^x=\log_6(2.5^x)\\ \log_66^x=\log_65^x\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x\log_66=\log_62+\log_65^x\\ x\log_66=x\log_65\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=\log_62+x\log_65\\ x=x\log_65\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x-x\log_65=\log_62\\ x-x\log_65=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x(1-\log_65)=\log_62\\ x(1-\log_65)=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=\dfrac{\log_62}{1-\log_65}\\ x=0\end{array} \right.\\ 13)\\ 6.5^x-5^{1-x}-1=0\\ \Leftrightarrow 5^x(6.5^x-5^{1-x}-1)=0.5^x\\ \Leftrightarrow 6.(5^x)^2-5-5^x=0\\ \Leftrightarrow 6.(5^x)^2-5^x-5=0\\ \Leftrightarrow 6.(5^x)^2-6.5^x+5.5^x-5=0\\ \Leftrightarrow 6.5^x(5^x-1)+5(5^x-1)=0\\ \Leftrightarrow (5^x-1)(6.5^x+5)=0\\ \Leftrightarrow 5^x-1=0(\text{Do} \ 6.5^x+5>0 \ \forall \ x)\\ \Leftrightarrow 5^x=1\\ \Leftrightarrow x=0$
