Question

1)d,e
2)e
3)h
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Answer 1

$1)d)lg \sqrt{ \frac{1}{100} } = lg \sqrt{ {100}^{ - 1} } = lg \sqrt{ { ({10}^{2}) }^{ - 1} }$

$= lg \sqrt{ {10}^{ - 2} } = lg {10}^{ - \frac{2}{2} } = lg {10}^{ - 1} = - 1$

$e)ln \frac{1}{ \sqrt{ \sqrt[4]{e} } } = ln \frac{1}{ \sqrt[8]{e} } = ln \frac{1}{ {e}^{ \frac{1}{8} } }$

$= ln {e}^{ - \frac{1}{8} } = - \frac{1}{8}$

$2)e) log_{ \sqrt{3} }(x + 5)$

$log_{a}(x) \: are \: sens \: daca \: :$

$a > 0,a \neq1$

$x > 0$

$\sqrt{3} > 0 \: (A), \sqrt{3} \neq1 \: (A)$

$x + 5 > 0$

$x > - 5$

$x \: \in \: ( - 5, + \infty )$

$3)h) log_{2}(4) + {( \frac{1}{4}) }^{ - 1} + \sqrt[3]{27}$

$= 2 + 4 + \sqrt[3]{ {3}^{3} }$

$= 6 + {3}^{ \frac{3}{3} }$

$= 6 + 3$

$= 9$