Ответы и объяснения

2014-01-19T17:08:56+00:00
1)  log₁/₂  \sqrt[3]{16} = x
    ( \frac{1}{2}) ^{X} =  \sqrt[3]{16}
 2^{-x} =  2^{ \frac{4}{3} }
x = - \frac{4}{3}
2)  ( \sqrt{b}) ^{x} =  \sqrt[7]{b}
    b^{ \frac{x}{2} } =  b^{ \frac{1}{7} }
x=  \frac{2}{7}
3)  ( \frac{1}{4}) ^{ log_{2}3 } =  2^{-2 log_{2}3 } =  2^{ log_{2} \frac{1}{9}  } =  \frac{1}{9}
4)  ( \sqrt{3}) ^{2+ log_{3}49 } =  3^{1+ log_{3}7 } =  3^{ log_{3}21 } = 21
5)  e^{3ln2} =  e^{ln8} = 8
6) log₈( log_{ \frac{1}{ \sqrt{5} } }  \frac{1}{5}  = log₈  \frac{1}{2} = - \frac{1}{3}
7) (lg8 + lg125)⁻³ = (lg 1000)⁻³ = 3⁻³ = 1/27
8)  \frac{ln27}{ln9} =  log_{9}27 =  \frac{ log_{3}27 }{ log_{3}9 } =  \frac{3}{2} = 1.5
9) ln12 *  \frac{ln e^{3} }{ln144} =  \frac{ln12*3}{2ln12} = 1.5
10)  \frac{ log_{3} \sqrt{5}  }{2} :  \frac{ log_{3}125 }{-3} =  \frac{ log_{3} \sqrt[4]{5}  }{ log_{3} \frac{1}{5}  } =  log_{ \frac{1}{5} }  \sqrt[4]{5} = - \frac{1}{4}
11)  log_{ \frac{3}{4} }  \frac{ \sqrt{3} }{2} =  \frac{1}{2}