Menu Close

Category: Logarithms

Question-121100

Question Number 121100 by Ar Brandon last updated on 05/Nov/20 Answered by TANMAY PANACEA last updated on 05/Nov/20 $$\frac{{logx}}{{x}\left({y}+{z}−{x}\right)}=\frac{{logy}}{{y}\left({z}+{x}−{y}\right)}=\frac{{logz}}{{z}\left({x}+{y}−{z}\right)}={k} \\ $$$${logx}={kx}\left({y}+{z}−{x}\right) \\ $$$${logy}={ky}\left({z}+{x}−{y}\right) \\ $$$${logz}={kz}\left({x}+{y}−{z}\right)…

Question-120927

Question Number 120927 by Ar Brandon last updated on 04/Nov/20 Answered by 675480065 last updated on 04/Nov/20 $$\mathrm{domain}:\:\mathrm{2x}−\mathrm{3}/\mathrm{4}\:>\mathrm{0}\:\cap\:\mathrm{x}>\mathrm{0}\:\cap\:\mathrm{x}>\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{x}>\mathrm{3}/\mathrm{8}\:\cap\:\mathrm{x}>\mathrm{0} \\ $$$$\mathrm{hence}\:\mathrm{2x}−\mathrm{3}/\mathrm{4}\:>\:\mathrm{x}^{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{3}/\mathrm{4}\:<\mathrm{0}…

Given-that-log-3x-1-2x-1-log-3x-1-5-find-the-value-of-x-

Question Number 54875 by shaddie last updated on 13/Feb/19 $$\mathrm{Given}\:\mathrm{that}\frac{\mathrm{log}\left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{2x}−\mathrm{1}} }{\mathrm{log}\left(\mathrm{3x}+\mathrm{1}\right)}=\mathrm{5},\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$ Answered by kaivan.ahmadi last updated on 14/Feb/19 $$\mathrm{log}\left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{2x}−\mathrm{1}} =\mathrm{log}\left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{5}} \Rightarrow \\ $$$$\left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{2x}−\mathrm{1}}…

Given-log-2-10-a-a-1-log-3-5-1-b-find-the-value-of-1-log-12-15-

Question Number 120380 by bramlexs22 last updated on 31/Oct/20 $${Given}\:\begin{cases}{\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{10}\right)=\frac{{a}}{{a}−\mathrm{1}}}\\{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{5}\right)=\frac{\mathrm{1}}{{b}}}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:\mathrm{1}+\mathrm{log}\:_{\mathrm{12}} \left(\mathrm{15}\right)\:? \\ $$ Answered by FelipeLz last updated on 31/Oct/20 $$\mathrm{log}_{\mathrm{2}}…

log-a-x-8-log-b-x-3-log-c-x-6-log-abc-x-

Question Number 120120 by benjo_mathlover last updated on 29/Oct/20 $$\begin{cases}{\mathrm{log}\:_{{a}} \left({x}\right)\:=\:\mathrm{8}}\\{\mathrm{log}\:_{{b}} \left({x}\right)\:=\:\mathrm{3}\:}\\{\mathrm{log}\:_{{c}} \left({x}\right)\:=\:\mathrm{6}}\end{cases}\:\Rightarrow\:\mathrm{log}\:_{{abc}} \:\left({x}\right)=? \\ $$ Answered by bemath last updated on 29/Oct/20 $$\begin{cases}{\mathrm{log}\:_{{a}} \left({x}\right)=\mathrm{8}\Rightarrow\mathrm{log}\:_{{x}}…

Given-a-b-c-real-number-and-not-equal-to-1-If-log-a-b-log-b-c-log-c-a-0-then-log-a-b-3-log-b-c-3-log-c-a-3-

Question Number 119802 by bemath last updated on 27/Oct/20 $${Given}\:{a},{b},{c}\:{real}\:{number}\:{and}\:{not}\:{equal}\:{to}\:\mathrm{1}. \\ $$$${If}\:\mathrm{log}\:_{{a}} \left({b}\right)+\mathrm{log}\:_{{b}} \left({c}\right)+\mathrm{log}\:_{{c}} \left({a}\right)=\mathrm{0}\:{then}\: \\ $$$$\left(\mathrm{log}\:_{{a}} \left({b}\right)\right)^{\mathrm{3}} +\left(\mathrm{log}\:_{{b}} \left({c}\right)\right)^{\mathrm{3}} +\left(\mathrm{log}\:_{{c}} \left({a}\right)\right)^{\mathrm{3}} =? \\ $$…

Given-that-1-log-3-x-log-27-y-express-y-in-terms-of-x-

Question Number 53675 by pieroo last updated on 24/Jan/19 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{1}+\mathrm{log}_{\mathrm{3}} \mathrm{x}\:=\mathrm{log}_{\mathrm{27}} \mathrm{y},\:\mathrm{express}\:\mathrm{y} \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{x}. \\ $$ Answered by kaivan.ahmadi last updated on 24/Jan/19 $$\mathrm{log}_{\mathrm{3}} \mathrm{3}+\mathrm{log}_{\mathrm{3}}…