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Category: Logarithms

express-the-following-in-form-of-log-a-f-x-i-4log-a-x-log-a-x-2-x-3-ii-log-a-x-log-a-x-3-

Question Number 9334 by j.masanja06@gmail.com last updated on 30/Nov/16 $$\mathrm{express}\:\mathrm{the}\:\mathrm{following}\:\mathrm{in}\:\mathrm{form}\:\mathrm{of}\:\mathrm{log}\:\mathrm{a}\left(\mathrm{f}\left(\mathrm{x}\right)\right) \\ $$$$\left(\mathrm{i}\right)\:\mathrm{4log}_{\mathrm{a}} \mathrm{x}−\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{3}} \right) \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{log}_{\mathrm{a}} \mathrm{x}\:+\:\:\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}+\mathrm{3}\right) \\ $$ Answered by mrW…

given-that-log-2-0-3-show-that-log-5-0-7-

Question Number 9333 by j.masanja06@gmail.com last updated on 30/Nov/16 $$\mathrm{given}\:\mathrm{that}\:\mathrm{log}\:\mathrm{2}=\mathrm{0}.\mathrm{3}.\mathrm{show}\:\mathrm{that}\:\mathrm{log}\:\mathrm{5}=\mathrm{0}.\mathrm{7} \\ $$ Answered by mrW last updated on 30/Nov/16 $$\mathrm{2}×\mathrm{5}=\mathrm{10} \\ $$$$\mathrm{log}\:\left(\mathrm{2}×\mathrm{5}\right)=\mathrm{log}\:\mathrm{10}=\mathrm{1} \\ $$$$\mathrm{log}\:\mathrm{2}+\mathrm{log}\:\mathrm{5}=\mathrm{1} \\…

evaluate-5-log-7-5-7-log-5-7-

Question Number 74753 by necxxx last updated on 30/Nov/19 $${evaluate}\:\mathrm{5}^{\sqrt{\mathrm{log}\:\mathrm{7}_{\mathrm{5}} }} \:−\:\mathrm{7}^{\sqrt{\mathrm{log}\:\mathrm{5}_{\mathrm{7}} }} \\ $$ Commented by mr W last updated on 30/Nov/19 $${what}\:{is}\:\mathrm{log}\:\mathrm{7}_{\mathrm{5}} ?\:{the}\:{same}\:{as}\:\mathrm{log}_{\mathrm{5}}…

Question-74589

Question Number 74589 by Aditya789 last updated on 27/Nov/19 Answered by MJS last updated on 27/Nov/19 $${a}\left({b}−{c}\right){x}^{\mathrm{2}} +{b}\left({c}−{a}\right){xy}+{c}\left({a}−{b}\right){y}^{\mathrm{2}} =\mathrm{0} \\ $$$${x}^{\mathrm{2}} +\frac{{b}\left({c}−{a}\right){y}}{{a}\left({b}−{c}\right)}{x}+\frac{{c}\left({a}−{b}\right){y}^{\mathrm{2}} }{{a}\left({b}−{c}\right)}=\mathrm{0} \\ $$$${x}={t}−\frac{{b}\left({c}−{a}\right){y}}{\mathrm{2}{a}\left({b}−{c}\right)}…

if-log-x-a-log-x-b-log-x-c-are-the-term-of-A-P-prove-that-c-2-ac-log-a-b-

Question Number 8893 by j.masanja06@gmail.com last updated on 04/Nov/16 $$\mathrm{if}\:\mathrm{log}_{\mathrm{x}} \mathrm{a},\mathrm{log}_{\mathrm{x}\:} \mathrm{b},\mathrm{log}_{\mathrm{x}} \mathrm{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{term}\:\mathrm{of}\:\mathrm{A}.\mathrm{P} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{c}^{\mathrm{2}} =\left(\mathrm{ac}\right)\mathrm{log}_{\mathrm{a}\:} \mathrm{b} \\ $$ Commented by j.masanja06@gmail.com last updated on…