共50条信息
若数列\(\left\{ {{\log }_{3}}{{a}_{n}} \right\}\)为等差数列,且\({{\log }_{3}}{{a}_{1}}+{{\log }_{3}}{{a}_{2}}+\cdots +{{\log }_{3}}{{a}_{10}}=10\),则\({{a}_{5}}{{a}_{6}}=\)___________.
设\(a{=}\log_{5}10{,}b{=}\log_{6}12{,}c{=}1{+}\log_{7}2\),则\(({ })\)
已知函数\(f(x)=\begin{cases} & \log \dfrac{1}{2}x,x > 0, \\ & \cos x,x\leqslant 0, \end{cases}\)则\(f\left( f\left( -\dfrac{\pi }{3} \right) \right)=\)________
已知\(a={{5}^{{lo}{{{g}}_{2}}3.4}}\),\(b={{5}^{{lo}{{{g}}_{4}}3.6}}\),\(c={{\left( \dfrac{1}{5} \right)}^{{lo}{{{g}}_{3}}0.3}}\),则\((\) \()\)
已知\(f(x)\)是定义在\(R\)上的周期为\(2\)的函数,当\(x∈(-1,1]\)时,\(f(x)=\begin{cases} -4x^{2}+ \dfrac{9}{8},-1 < x\leqslant 0, \\ \log _{2}x,0 < x\leqslant 1, \end{cases}\),则\(f(f( \dfrac{7}{2}))=\)________.
用\(\lg \) \(x\),\(\lg \) \(y\),\(\lg \) \(z\)表示下列各式:
\((1)\lg (\)\(xyz\)\()\);
\((2)\lg \dfrac{xy^{2}}{z}\);
\((3)\lg \dfrac{xy^{3}}{ \sqrt{z}}\);
\((4)\lg \dfrac{ \sqrt{x}}{y^{2}z}\).
\(\sqrt[3]{({-}4)^{3}}{+}({-}\dfrac{1}{8})^{{-}\frac{4}{3}}{+}(\lg 2)^{2}{+}\lg 5{⋅}\lg 20{=}\) ______ .
\((1){{0.027}^{{--}\frac{1}{3}}}-{{(-\dfrac{1}{7})}^{-2}}+{{256}^{\frac{3}{4}}}-{{3}^{-1}}+{{(\sqrt{2}-1)}^{0}}\);
\((2)\dfrac{\lg 8+\lg 125-\lg 2-\lg 5}{\lg \sqrt{10}\lg 0.1}\)。
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