Question

Exercitiile 26 și 27 va rog frumos care știți! Mulțumesc!

Answer 1

26)

$a)\quad \log_3 1 < \log_3 2<\log _3 3,\quad 3>1 \\ \\ \Rightarrow 0 < \log_3 2< 1\quad (A) \\ \\ b)\quad 1<\log_3 4<\dfrac{3}{2}\,\Bigg|3^{()}\\ \\ 3^1 <3^{\log_3 4}<3^{\frac{3}{2}} \\ \\ 3<4<3^{\frac{3}{2}} \\ \\ \sqrt{9}<\sqrt{16}<\sqrt{27}\quad (A)$

27)

$a) \quad \dfrac{3}{2}<\log_{2}3<2\,\Bigg|2^{()} \\ \\ 2^{\frac{3}{2}}<2^{\log_{2}3}<2^2 \\ \\ \sqrt{2^3}<3<2^2\\ \\\sqrt{8}< \sqrt{9}< \sqrt{16}\quad (A)\\ \\ \\ b) \quad a = \log_{2}3+\log_3 2 \\ \\ \dfrac{3}{2}<\log_{2}3<2\,\,\,(*) \\ \\ \dfrac{1}{2}<\log_{3}2<1\,\,\,(**) \, \Rightarrow 3^{\frac{1}{2}}<3^{\log_{3}2}<3^1 \Rightarrow \sqrt{3}<\sqrt{4}<\sqrt{9}\quad (A)$

$\text{Din }(*) + (**): \\ \\ \Rightarrow \dfrac{3}{2}+\dfrac{1}{2}<\log_{2}3+\log_{3}2<2+1\\ \\ \Rightarrow 2<\log_{2}3+\log_{3}2<3 \\ \\ \\\Rightarrow \big[a\big] = 2$