Câu 1 :
\(...\Rightarrow A=3^{\left(3+\sqrt{2}-1+\sqrt{2}+2-2\sqrt{2}\right)}=3^4=81\)
Câu 2 :
a) \(log_3\dfrac{5}{9}-2log_3\sqrt{5}=log_35-log_33^2-log_35=-2log_33=-2\)
b) \(4log_{12}2+2log_{12}3=log_{12}2^4+log_{12}3^2=log_{12}\left(2^4.3^2\right)=log_{12}144=log_{12}12^2=2\)
Câu 3 :
\(log_5\left(x-1\right)+log_5\left(x-3\right)=log_5\left(2x+10\right)\left(1\right)\)
\(Đk:\left\{{}\begin{matrix}x-1>0\\x-3>0\\2x+10>0\end{matrix}\right.\) \(\Leftrightarrow x>3\)
\(\left(1\right)\Leftrightarrow log_5\left(x-1\right)\left(x-3\right)=log_5\left(2x+10\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=2x+10\)
\(\Leftrightarrow x^2-4x+3=2x+10\)
\(\Leftrightarrow x^2-6x-7=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\left(loại\right)\\x=7\end{matrix}\right.\) \(\Leftrightarrow x=7\) (so với đk \(x>3\) phù hợp)
