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Category: Logarithms

Choose-the-correct-option-If-a-b-and-c-are-consecutive-positive-integers-and-log-1-ac-2k-then-the-value-of-k-is-a-log-a-b-log-b-c-2-d-1-Give-the-explaination-also-

Question Number 193230 by MATHEMATICSAM last updated on 07/Jun/23 $$\boldsymbol{\mathrm{Choose}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{option}}: \\ $$$$\mathrm{If}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{consecutive}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{log}\left(\mathrm{1}\:+\:{ac}\right)\:=\:\mathrm{2}{k}\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{is}: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{log}\:{a} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{log}\:{b} \\ $$$$\left.\mathrm{c}\right)\:\mathrm{2} \\ $$$$\left.\mathrm{d}\right)\:\mathrm{1} \\…

There-exists-a-unique-positive-integer-a-for-which-The-sum-u-n-1-2023-n-2-na-5-is-an-integer-strictly-between-1000-amp-1000-find-a-u-

Question Number 193183 by York12 last updated on 06/Jun/23 $$ \\ $$$${There}\:{exists}\:{a}\:{unique}\:{positive}\:{integer}\:{a}\:{for} \\ $$$${which}\:{The}\:{sum}\:{u}\:\:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\lfloor\frac{{n}^{\mathrm{2}} −{na}}{\mathrm{5}}\rfloor\:{is}\:{an}\:{integer} \\ $$$${strictly}\:{between}\:−\mathrm{1000}\:\&\:\mathrm{1000}\:{find}\:{a}+{u}. \\ $$ Answered by York12 last…

Question-65333

Question Number 65333 by aliesam last updated on 28/Jul/19 Commented by Prithwish sen last updated on 28/Jul/19 $$\mathrm{log}_{\mathrm{y}} \mathrm{x}=\mathrm{v}\Rightarrow\frac{\mathrm{v}^{\mathrm{2}} +\mathrm{1}}{\mathrm{v}}\:=\:\frac{\mathrm{17}}{\mathrm{4}}\Rightarrow\mathrm{4v}^{\mathrm{2}} −\mathrm{17v}+\mathrm{4}=\mathrm{0} \\ $$$$\mathrm{4v}^{\mathrm{2}} −\mathrm{16v}−\mathrm{v}+\mathrm{4}=\mathrm{0}\Rightarrow\mathrm{4v}\left(\mathrm{v}−\mathrm{4}\right)−\mathrm{1}\left(\mathrm{v}−\mathrm{4}\right)=\mathrm{0} \\…

log-x-x-2-2-x-3-3-x-4-4-

Question Number 130553 by Study last updated on 26/Jan/21 $${log}\left({x}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}}+\frac{{x}^{\mathrm{4}} }{\mathrm{4}}+….\right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21 $${log}\left(−{log}\left(\mathrm{1}−{x}\right)\right)={log}\left({log}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)\right) \\…

Question-64785

Question Number 64785 by Rio Michael last updated on 21/Jul/19 Answered by LPM last updated on 21/Jul/19 $$\left.\mathrm{1}\right)\:\mathrm{x}_{\mathrm{n}} \leqslant\:\mathrm{2}\:,\forall\:\mathrm{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{x}_{\mathrm{n}} \leqslant\mathrm{x}_{\mathrm{n}+\mathrm{1}} ,\:\forall\:\mathrm{n}\geqslant\mathrm{1} \\ $$$$\:\Rightarrow\:\mathrm{x}_{\mathrm{n}}…

Question-130244

Question Number 130244 by Adel last updated on 23/Jan/21 Commented by mr W last updated on 23/Jan/21 $${it}'{s}\:{not}\:{to}\:{understand}:\:{this}\:{question} \\ $$$${is}\:{asked}\:{already}\:{four}\:{times},\:{three} \\ $$$${times}\:{alone}\:{from}\:{you}!\:{what}'{s}\:{the} \\ $$$${sense}?\:{if}\:{you}\:{don}'{t}\:{understand}\:{the} \\…

log-12-x-x-1-4-log-9-x-x-

Question Number 129451 by bemath last updated on 15/Jan/21 $$\:\mathrm{log}\:_{\mathrm{12}} \left(\sqrt{\mathrm{x}}\:+\:\sqrt[{\mathrm{4}}]{\mathrm{x}}\:\right)\:=\:\mathrm{log}\:_{\mathrm{9}} \left(\sqrt{\mathrm{x}}\:\right)\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$ Answered by liberty last updated on 16/Jan/21 $$\:\mathrm{log}\:_{\mathrm{12}} \left(\sqrt{\mathrm{x}}\:+\:\sqrt[{\mathrm{4}}]{\mathrm{x}}\:\right)\:=\:\mathrm{log}\:_{\mathrm{3}}…

Question-129088

Question Number 129088 by Gulnoza last updated on 12/Jan/21 Answered by MJS_new last updated on 12/Jan/21 $$\mathrm{4}^{\mathrm{2log}_{\mathrm{4}} \:{x}} =\left(\mathrm{4}^{\mathrm{log}_{\mathrm{4}} \:{x}} \right)^{\mathrm{2}} ={x}^{\mathrm{2}} =\mathrm{25} \\ $$$$\Rightarrow\:{x}=\pm\mathrm{5}…