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August 2022 1 11 Report

Вычислите:
1. [tex] \frac{log _{4} 36}{log _{4}6 } [/tex]
2. [tex] \frac{log _{0,3}32 }{log _{0,3} 64} [/tex]
3. [tex] \frac{2log _{0,5}2+log _{0,5} \sqrt{10} }{ log_{0,5} 10- log_{0,5} \sqrt{10} + log_{0,5} 4} [/tex]
4. [tex] \frac{ log_{0,3}16 }{ log_{0,3} 15- log_{0,3} 30} [/tex]

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arsenlevadniy

Verified answer

$\frac{log _{4}36}{log _{4}6} = \frac{log _{4}6^2}{log _{4}6} = \frac{2log _{4}6}{log _{4}6} = 2;$

$\frac{log _{0,3}32}{log _{0,3}64} = \frac{log _{0,3}2^5}{log _{0,3}2^6} = \frac{5log _{0,3}2}{6log _{0,3}2} = \frac{5}{6};$

$\frac{2log _{0,5}2+log _{0,5}\sqrt{10}}{log_{0,5}10-log_{0,5}\sqrt{10}+log_{0,5}4} = \frac{log _{0,5}(2^2\cdot\sqrt{10})}{log_{0,5} \frac{10\cdot4}{\sqrt{10}} } = \frac{log _{0,5}(4\cdot\sqrt{10})}{log _{0,5}(4\cdot\sqrt{10})} = 1;$

$\frac{log_{0,3}16}{log_{0,3}15-log_{0,3}30} = \frac{log_{0,3}2^4}{log_{0,3}\frac{15}{30}} = \frac{4log_{0,3}2}{log_{0,3}2^{-1}} = \frac{4log_{0,3}2}{-log_{0,3}2}} = -4.$

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