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Category: Logarithms

x-log-xy-y-log-xy-x-log-x-y-y-log-x-y-0-find-x-y-

Question Number 85826 by jagoll last updated on 25/Mar/20 $$\:^{\mathrm{x}} \mathrm{log}\:\left(\mathrm{xy}\right).\:^{\mathrm{y}} \mathrm{log}\:\left(\mathrm{xy}\right)\:+\:^{\mathrm{x}} \mathrm{log}\:\left(\mathrm{x}−\mathrm{y}\right).^{\mathrm{y}} \mathrm{log}\:\left(\mathrm{x}−\mathrm{y}\right)=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{x}+\mathrm{y}\: \\ $$ Commented by john santu last updated on…

y-2-1-log-x-8-then-x-

Question Number 20245 by virus last updated on 24/Aug/17 $$\mathrm{y}=\mathrm{2}^{\frac{\mathrm{1}}{{log}_{{x}} \mathrm{8}}} \\ $$$${then}\:{x}=? \\ $$ Answered by Tinkutara last updated on 24/Aug/17 $${y}\:=\:\mathrm{2}^{\mathrm{log}_{\mathrm{8}} \:{x}} \:=\:\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{log}_{\mathrm{2}}…

log-x-x-3-7-lt-log-x-3-7-

Question Number 85694 by john santu last updated on 24/Mar/20 $$\mathrm{log}_{\left(\frac{{x}}{{x}−\mathrm{3}}\right)} \left(\mathrm{7}\right)\:<\:\mathrm{log}_{\left(\frac{{x}}{\mathrm{3}}\right)} \:\left(\mathrm{7}\right)\: \\ $$ Commented by jagoll last updated on 24/Mar/20 $$\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{7}} \left(\frac{\mathrm{x}}{\mathrm{x}−\mathrm{3}}\right)}\:<\:\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{7}} \left(\frac{\mathrm{x}}{\mathrm{3}}\right)}…