优优班--学霸训练营 > 知识点挑题
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            • 1.
              设实数\(a\),\(b\),\(c\),\(d\)满足\(b\neq 0,d\neq -1,{且} \dfrac {a^{2}-\ln a}{b}= \dfrac {c-1}{d+1}=1\),则\((a-c)^{2}+(b-d)^{2}\)的最小值是\((\)  \()\)
              A.\(2\)
              B.\(1\)
              C.\( \dfrac {1}{2}\)
              D.\( \dfrac {1}{4}\)
            • 2.
              若\(|\log _{a} \dfrac {1}{4}|=\log _{a} \dfrac {1}{4}\),且\(|\log _{b}a|=-\log _{b}a\),则\(a\),\(b\)满足的关系式是\((\)  \()\)
              A.\(1 < a\),\(1 < b\)
              B.\(1 < a\)且\(0 < b < 1\)
              C.\(1 < b\)且\(0 < a < 1\)
              D.\(0 < a < 1\)且\(0 < b < 1\)
            • 3.
              计算:\( \sqrt[5]{2}×(4\;^{- \frac {2}{5}})^{-1}+\lg \sqrt {1000}-\sin 270^{\circ}=\) ______ .
            • 4.
              计算\((\lg \dfrac {1}{4}-\lg 25)÷100^{- \frac {1}{2}}=\) ______ .
            • 5.
              计算:\(( \dfrac {2}{3})^{0}+3×( \dfrac {9}{4})^{- \frac {1}{2}}+(\lg 4+\lg 25)\)的值是 ______ .
            • 6.
              设\(a=\log _{3}π\),\(b=\log \;_{ \frac {1}{3}}π\),\(c=π^{-3}\),则\((\)  \()\)
              A.\(a > b > c\)
              B.\(b > a > c\)
              C.\(a > c > b\)
              D.\(c > b > a\)
            • 7.
              已知函数\(f(x)=-x^{2}-2x\),设\(a=\ln 2\),\(b=\log \;_{ \frac {1}{3}}2\),\(c=3\;^{ \frac {1}{2}}\),则必有\((\)  \()\)
              A.\(f(b) > f(a) > f(c)\)
              B.\(f(c) > f(a) > f(b)\)
              C.\(f(a) > f(b) > f(c)\)
              D.\(f(b) > f(c) > f(a)\)
            • 8.
              若正数\(a\),\(b\)满足\(\log _{2}a=\log _{5}b=\lg (a+b)\),则\( \dfrac {1}{a}+ \dfrac {1}{b}\)的值为 ______
            • 9.
              在各项均为正数的等比数列\(\{a_{n}\}\)中,若\(a_{3}a_{8}=9\),则\(\log _{3}a_{1}+\log _{3}a_{10}=(\)  \()\)
              A.\(1\)
              B.\(2\)
              C.\(4\)
              D.\(\log _{3}5\)
            • 10. (2016•浙江)已知a>b>1,若logab+logba= ,ab=ba , 则a= , b=
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