\(a+b=2\sqrt{ab}\)
=>\(a-2\sqrt{ab}+b=0\)
=>\(\left(\sqrt{a}-\sqrt{b}\right)^2=0\)
=>a=b
\(ln\sqrt{a}+ln\sqrt{b}=ln\left(\sqrt{ab}\right)=ln\left(\sqrt{a\cdot a}\right)=lna\)
\(\dfrac{1}{4}\left(lna+lnb\right)=\dfrac{1}{4}\left(lnab\right)=\dfrac{1}{4}\left(lna^2\right)=\dfrac{1}{4}\cdot2\cdot lna=\dfrac{1}{2}\cdot lna\)
=>Loại C
\(ln\left(\sqrt{a}+\sqrt{b}\right)=ln\left(\sqrt{a}+\sqrt{a}\right)=ln\left(2\sqrt{a}\right)\)
=>Loại B
\(ln\left(\dfrac{\sqrt{a}+\sqrt{b}}{2}\right)=ln\left(\dfrac{\sqrt{a}+\sqrt{a}}{2}\right)=ln\sqrt{a}=\dfrac{1}{2}\cdot lna\)
=>Chọn A
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