hhhuuu cuu mình với
Câu 1: Tính: \( A = a^{\frac{1}{3}} \cdot a^{\frac{3}{2}} \cdot a^{\frac{2}{3}} \)
Câu 2: Tính giá trị biểu thức:
a/ \( \log_2 \frac{16}{3} + 2\log_2 \sqrt{6} \)
b/ \( \log_5 15 + \log_5 \sqrt{12} \)
Câu 3: Giải phương trình:
a/ \( \log_9 x = \frac{1}{2} \)
b/ \( \log_{\frac{1}{2}} (3x + 1) = \log_{\frac{1}{2}} (4x - 1) \)
c/ \( \log_2 x + \log_2 (x - 3) = 1 \)
Câu 1 :
\(A=a^{\dfrac{1}{3}}:a^{\dfrac{3}{2}}.a^{\dfrac{2}{3}}=a^{\left(\dfrac{1}{3}-\dfrac{3}{2}+\dfrac{2}{3}\right)}=a^{-\dfrac{1}{2}}=\dfrac{1}{\sqrt{a}}\)
Câu 2 :
a) \(log_2\dfrac{16}{3}+2log_2\sqrt{6}=log_2\dfrac{16}{3}+log_26=log_2\left(\dfrac{16}{3}.6\right)=log_232=log_22^5=5\)
b) \(log_515+log_5\sqrt{12}=log_5\left(15.\sqrt{12}\right)=log_530\sqrt{3}\)
Câu 3 :
a) \(log_9x=\dfrac{1}{2}\Rightarrow x=9^{\dfrac{1}{2}}=\sqrt{9}=3\)
b) \(log_{\dfrac{1}{2}}\left(3x+1\right)=log_{\dfrac{1}{2}}\left(4x-1\right)\left(1\right)\)
\(Đk:\left\{{}\begin{matrix}3x+1>0\\4x-1>0\end{matrix}\right.\) \(\Leftrightarrow x>\dfrac{1}{4}\)
\(\left(1\right)\Leftrightarrow3x+1=4x-1\)
\(\Leftrightarrow x=-2\left(loại\right)\)
\(\Leftrightarrow x\in\varnothing\)
c) \(log_2x+log_2\left(x-3\right)=1\left(x>3\right)\)
\(\Leftrightarrow log_2x\left(x-3\right)=1\)
\(\Leftrightarrow x\left(x-3\right)=2^1\)
\(\Leftrightarrow x^2-3x-2=0\)
\(\Leftrightarrow x=\dfrac{3\pm\sqrt{17}}{2}\) so với \(x>3\Rightarrow x=\dfrac{3+\sqrt{17}}{2}\)
