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Question Number 181154 by mathlove last updated on 22/Nov/22
(log_(15) 5)^2 +(log_(15) 3)(log_(15) 75)=?
$$\left({log}_{\mathrm{15}} \mathrm{5}\right)^{\mathrm{2}} +\left({log}_{\mathrm{15}} \mathrm{3}\right)\left({log}_{\mathrm{15}} \mathrm{75}\right)=? \\ $$$$ \\ $$
Answered by SEKRET last updated on 22/Nov/22
log_(15) (3)=a      log_(15) ^(  ) (5)= 1−a  log_(15) (15∙5)=1+log_(15) (5)=2−a   (1−a)^2 +a∙(2−a)=a^2 −2a+1+2a−a^2 =1  answer  1     ABDULAZIZ    ABDUVALIYEV
$$\boldsymbol{\mathrm{log}}_{\mathrm{15}} \left(\mathrm{3}\right)=\boldsymbol{\mathrm{a}}\:\:\:\:\:\:\boldsymbol{\mathrm{log}}_{\mathrm{15}} ^{\:\:} \left(\mathrm{5}\right)=\:\mathrm{1}−\boldsymbol{\mathrm{a}} \\ $$$$\boldsymbol{\mathrm{log}}_{\mathrm{15}} \left(\mathrm{15}\centerdot\mathrm{5}\right)=\mathrm{1}+\boldsymbol{\mathrm{log}}_{\mathrm{15}} \left(\mathrm{5}\right)=\mathrm{2}−\boldsymbol{\mathrm{a}} \\ $$$$\:\left(\mathrm{1}−\boldsymbol{\mathrm{a}}\right)^{\mathrm{2}} +\boldsymbol{\mathrm{a}}\centerdot\left(\mathrm{2}−\boldsymbol{\mathrm{a}}\right)=\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{\mathrm{a}}+\mathrm{1}+\mathrm{2}\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{a}}^{\mathrm{2}} =\mathrm{1} \\ $$$$\boldsymbol{\mathrm{answer}}\:\:\mathrm{1}\: \\ $$$$\:\:\boldsymbol{{ABDULAZIZ}}\:\:\:\:\boldsymbol{{ABDUVALIYEV}} \\ $$
Commented by mathlove last updated on 22/Nov/22
thanks
$${thanks} \\ $$

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