a

\(71-\left(33+x\right)=26\\ \Rightarrow71-33-x=26\\ \Rightarrow38-x=26\\ \Rightarrow x=38-26\\ \Rightarrow x=12\)

b

\(\left(x+73\right)-26=74\\ \Rightarrow x+73=74+26\\ \Rightarrow x+73=100\\ \Rightarrow x=100-73\\ \Rightarrow x=27\)

c

\(\left(9-x\right)^3=216\\ \Rightarrow\left(9-x\right)^3=6^3\)

\(\Rightarrow\) \(9-x=6\) 

\(\Rightarrow x=9-6=3\)

d

\(5.3^{x+1}=135\\ \Rightarrow3^{x+1}=\dfrac{135}{5}=27\\ \Rightarrow3^{x+1}=3^3\\ \Rightarrow x+1=3\\ \Rightarrow x=3-1\\ \Rightarrow x=2\)

2 will visit (TLĐ: tomorrow)

3 will have (on the weekend: cuối tuần => TLĐ)

4 produce (HTĐ: every year)

5 are wasting (HTTD: at the moment)

Có:

\(3^2=9\\ 3^3=27\\ 3^4=81\\ 3^5=243\\ 3^6=729\)

Từ trên thấy có với số mũ \(n=3;4;5\) thì thỏa mãn \(25< 3^n< 250\)

Vậy \(3^n=\left\{{}\begin{matrix}3^3=27\\3^4=81\\3^5=243\end{matrix}\right.\)

\(n=\left\{{}\begin{matrix}3\\4\\5\end{matrix}\right.\)

1

ĐK: `x>1`

PT trở thành:

\(\sqrt{\dfrac{2x-3}{x-1}}=2\\ \Leftrightarrow\dfrac{2x-3}{x-1}=2^2=4\\ \Leftrightarrow4x-4-2x+3=0\\ \Leftrightarrow2x-1=0\\ \Leftrightarrow x=\dfrac{1}{2}\left(KTM\right)\)

Vậy PT vô nghiệm.

b

ĐK: \(x\ge2\)

Đặt \(t=\sqrt{x-2}\) (\(t\ge0\))

=> \(x=t^2+2\)

PT trở thành: \(t^2+2-5t+2=0\)

\(\Leftrightarrow t^2-5t+4=0\)

nhẩm nghiệm: `a+b+c=0` (`1+(-5)+4=0`)

\(\Rightarrow\left\{{}\begin{matrix}t=1\left(nhận\right)\\t=4\left(nhận\right)\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-2}=1\\\sqrt{x-2}=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=3\left(TM\right)\\x=18\left(TM\right)\end{matrix}\right.\)

3

\(A=sin\left(x+\dfrac{\pi}{4}\right).cos\left(x-\dfrac{\pi}{4}\right)\\ =\dfrac{1}{2}\left[sin\left(x+\dfrac{\pi}{4}+x-\dfrac{\pi}{4}\right)+sin\left(x+\dfrac{\pi}{4}-x+\dfrac{\pi}{4}\right)\right]\\ =\dfrac{1}{2}\left(sin2x+sin\dfrac{\pi}{2}\right)\\ =\dfrac{1}{2}\left(-\dfrac{1}{3}+1\right)\\ =\dfrac{1}{3}\)

ĐK: \(x\ge0;x\ne4\)

Khi đó:

\(M=\left(\dfrac{\sqrt{x}+2}{x-4}+\dfrac{\sqrt{x}-2}{x-4}\right).\dfrac{x-4}{4}\\ =\left(\dfrac{\sqrt{x}+2+\sqrt{x}-2}{x-4}\right).\dfrac{x-4}{4}\\ =\dfrac{2\sqrt{x}\left(x-4\right)}{\left(x-4\right).2.2}\\ =\dfrac{\sqrt{x}}{2}\)

\(\left(x-1\right)^2=25\\ \Rightarrow\left(x-1\right)^2=5^2\\ \Rightarrow x-1=5\\ \Rightarrow x=6\)

\(3^x=27\\ \Rightarrow3^x=3^3\\ \Rightarrow x=3\)

\(2^{x-1}=32\\ \Rightarrow2^{x-1}=2^5\\ \Rightarrow x-1=5\\ \Rightarrow x=6\)

\(3^{x-2}=81\\ \Rightarrow3^{x-2}=3^4\\ \Rightarrow x-2=4\\ \Rightarrow x=6\)

3

Điều chế dung dịch kiềm từ `Na_2O`:

\(Na_2O+H_2O\rightarrow2NaOH\)

Điều chế dung dịch kiềm từ `BaO`:

\(BaO+H_2O\rightarrow Ba\left(OH\right)_2\)

Điều chế dung dịch kiềm từ `K_2O`:

\(K_2O+H_2O\rightarrow2KOH\)