E-log-a-c-b-log-ab-c-log-b-c-a-log-ab-c-

Question Number 139456 by SOMEDAVONG last updated on 27/Apr/21

E = \log_{a} \sqrt{\frac{c}{b^{\log_{ab} c}}} + \log_{b} \sqrt{\frac{c}{a^{\log_{ab} c}}}

Answered by bemath last updated on 27/Apr/21

E = \log_{a} \sqrt{\frac{c}{c^{\log_{ab} b}}} + \log_{b} \sqrt{\frac{c}{c^{\log_{ab} a}}}

E = \frac{1}{2} [\log_{a} (c^{1 - \log_{ab} b}) + \log_{b} (c^{1 - \log_{ab} a})]

E = \frac{1}{2} [\log_{a} (c^{\log_{ab} (\frac{1}{a})}) + \log_{b} (c^{\log_{ab} (\frac{1}{b})})]

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