Menu Close

Category: Logarithms

Question-194961

Question Number 194961 by SirMUTUKU last updated on 20/Jul/23 Answered by mahdipoor last updated on 20/Jul/23 $${log}\mathrm{225}={log}\left(\mathrm{25}×\mathrm{9}\right)={log}\frac{\mathrm{100}}{\mathrm{4}}+{log}\mathrm{9}= \\ $$$${log}\mathrm{100}−{log}\mathrm{4}+\mathrm{2}{log}\mathrm{3}=\mathrm{2}−.\mathrm{6021}+\mathrm{2}×.\mathrm{4771}= \\ $$$$\mathrm{2}.\mathrm{3521} \\ $$ Terms of…

Question-194613

Question Number 194613 by cortano12 last updated on 11/Jul/23 $$\:\:\:\:\:\:\cancel{\underline{ }} \\ $$ Answered by MM42 last updated on 11/Jul/23 $$\frac{\mathrm{1}}{{log}_{{x}} \mathrm{4}{x}}+\frac{\mathrm{1}}{{log}_{{x}} \frac{{x}}{\mathrm{2}}}=\mathrm{2} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}{log}_{{x}}…

Question-194165

Question Number 194165 by pascal889 last updated on 29/Jun/23 Answered by qaz last updated on 29/Jun/23 $${log}_{\mathrm{2}} \mathrm{4096}+\left[\mathrm{4}\left({log}_{\mathrm{2}} {x}\right)^{\mathrm{3}} −\mathrm{16}{log}_{\mathrm{2}} {x}\right]{log}_{\mathrm{2}} {x}=\mathrm{0} \\ $$$${log}_{\mathrm{2}} {x}={y}\:\:\:\:,\mathrm{12}+\mathrm{4}{y}^{\mathrm{4}}…

Find-the-value-of-x-from-the-following-equations-4-x-y-y-x-32-log-3-x-y-log-3-x-y-1-

Question Number 193295 by MATHEMATICSAM last updated on 09/Jun/23 $$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}}\:\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}} \\ $$$$\boldsymbol{\mathrm{equations}}: \\ $$$$\mathrm{4}^{\frac{{x}}{{y}}\:+\:\frac{{y}}{{x}}} \:=\:\mathrm{32} \\ $$$$\mathrm{log}_{\mathrm{3}} \left({x}\:−\:{y}\right)\:+\:\mathrm{log}_{\mathrm{3}} \left({x}\:+\:{y}\right)\:=\:\mathrm{1} \\ $$ Answered by BaliramKumar last…

Select-the-correct-option-with-explaination-If-1-3-log-3-M-3log-3-N-1-log-0-008-5-then-a-M-9-9-N-b-N-9-9-M-c-M-3-3-N-d-N-3-3-M-

Question Number 193253 by MATHEMATICSAM last updated on 08/Jun/23 $$\boldsymbol{\mathrm{Select}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{option}}\:\boldsymbol{\mathrm{with}}\: \\ $$$$\boldsymbol{\mathrm{explaination}}: \\ $$$$\mathrm{If}\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{log}_{\mathrm{3}} {M}\:+\:\mathrm{3log}_{\mathrm{3}} {N}\:=\:\mathrm{1}\:+\:\mathrm{log}_{\mathrm{0}.\mathrm{008}} \mathrm{5}\:\mathrm{then} \\ $$$$\mathrm{a}.\:{M}^{\mathrm{9}} \:=\:\frac{\mathrm{9}}{{N}} \\ $$$$\mathrm{b}.\:{N}^{\mathrm{9}} \:=\:\frac{\mathrm{9}}{{M}} \\ $$$$\mathrm{c}.\:{M}^{\mathrm{3}}…

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…