1, Cho $\log _25$ = a, $\log_\sqrt{27}8$ = b. Tính $\log _{25}45$
2, Cho $\log_9 50$ = a, $\log_\sqrt{27} 40$ = b. Tính $\log_{25} 80$
3, CHo $\log _52$ = a, $\log _53$ = b. Tính: $\log_5 27$; $\log_5 15$; $\log_5 12$; $\log_5 30$
3. Ta có:
$\log_527=3\log_53=3b$
$\log_515=1+\log_53=1+b$
$\log_512=2\log_52+\log_53=2a+b$
$\log_530=1+\log_52+\log_53=1+a+b$
2.
Ta có:
$\log_{25}80=\dfrac{1}{2}\log_580=\dfrac{1}{2}(1+4\log_52)$
$b=\log_{\sqrt{27}}40=2\log_{27}40=2(\log_{27}8+\log_{27}5)=2(\log_32+\dfrac{1}{3}\log_35)$
$a=\log_950=\dfrac{1}{2}\log_350=\dfrac{1}{2}(\log_32+2\log_25)$
$\Rightarrow \left\{\begin{array}{l}\log_32=\dfrac{3b-2a}{5}\\\log_35=\dfrac{12a-3b}{10}\end{array}\right.$
$\Rightarrow \log_52=\dfrac{\log_32}{\log_35}=\dfrac{6b-4a}{12a-3b}$
$\Rightarrow \log_{25}80=\dfrac{1}{2}+\dfrac{12b-8a}{12a-3b}$
1.
Ta có:
$\log_{25}45=\dfrac{1}{2}\log_545=\dfrac{1}{2}(1+2\log_53)$
$b=\log_{\sqrt{27}}8=2\log_{27}8=2\log_32=\dfrac{2}{\log_23} \Rightarrow \log_23=\dfrac{2}{b}$
$\Rightarrow \log_53=\dfrac{\log_23}{\log_25}=\dfrac{2}{ab}$
$\Rightarrow \log_{25}{45}=\dfrac{1}{2}+\dfrac{2}{ab}$
1) $\log_{\sqrt{27}} 8 = 2\log_3 2 = b \Rightarrow \log_3 2 = \dfrac{b}{2} \Rightarrow \log_2 3 = \dfrac{2}{b}$

$\log_{25} 45 = \log_5 3 + \dfrac{1}{2} = \dfrac{1}{2} +  \dfrac{\log_2 3}{\log_2 5}$

KQ $= \dfrac{1}{2} + \dfrac{2}{ab} $

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