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Category: Logarithms

Question-109963

Question Number 109963 by bobhans last updated on 26/Aug/20 Answered by bemath last updated on 26/Aug/20 $$\left(\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}}\:=\:\sqrt{\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{1}}\:\geqslant\:\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{10}}\:=\sqrt{\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{9}}\:\geqslant\:\mathrm{3} \\ $$$$\Leftrightarrow\:\mathrm{log}\:_{\mathrm{3}}…

log-3-a-1-log-4-a-8-a-

Question Number 175104 by blackmamba last updated on 19/Aug/22 $$\:\:\mathrm{log}\:_{\mathrm{3}} \left({a}+\mathrm{1}\right)=\mathrm{log}\:_{\mathrm{4}} \left({a}+\mathrm{8}\right) \\ $$$$\:{a}=? \\ $$ Answered by MJS_new last updated on 19/Aug/22 $${a}+\mathrm{8}=\mathrm{4}^{{x}} \wedge{a}+\mathrm{1}=\mathrm{3}^{{x}}…