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Category: Logarithms

if-log-6-45-x-log-18-24-y-then-log-12-25-in-terms-of-x-y-

Question Number 25593 by behi.8.3.4.17@gmail.com last updated on 11/Dec/17 $$\boldsymbol{{if}}\:\::\:\:\:\boldsymbol{{log}}_{\mathrm{6}} ^{\mathrm{45}} =\boldsymbol{{x}}\:\:,\:\:\:\boldsymbol{{log}}_{\mathrm{18}} ^{\mathrm{24}} =\boldsymbol{{y}} \\ $$$$\boldsymbol{{then}}\::\:\:\:\boldsymbol{{log}}\:_{\mathrm{12}} ^{\mathrm{25}} \:=?\left(\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{x},\mathrm{y}\right) \\ $$ Answered by Rasheed.Sindhi last updated…

log-x-4-x-2-8x-12-lt-1-2-log-x-2-2-x-2-

Question Number 90806 by john santu last updated on 26/Apr/20 $$\mathrm{log}_{\left({x}+\mathrm{4}\right)} \left({x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{12}\right)\:<\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}_{\mid{x}−\mathrm{2}\mid} \left(\mathrm{2}−{x}\right)^{\mathrm{2}} \\ $$ Commented by john santu last updated on 26/Apr/20 $$\Rightarrow\left(\mathrm{2}−{x}\right)^{\mathrm{2}}…

log-5-x-9-log-5-3x-2-12-log-5-2x-1-0-

Question Number 156109 by cortano last updated on 08/Oct/21 $$\:\:\mathrm{log}\:_{\mathrm{5}} \left(\sqrt{\mathrm{x}−\mathrm{9}}\right)−\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{3x}^{\mathrm{2}} −\mathrm{12}\right)−\mathrm{log}\:_{\mathrm{5}} \left(\sqrt{\mathrm{2x}−\mathrm{1}}\right)\:\leqslant\:\mathrm{0} \\ $$ Answered by yeti123 last updated on 08/Oct/21 $$\left(\mathrm{1}\right)\:\cap\:\left(\mathrm{2}\right)\:\cap\:\left(\mathrm{3}\right)\:\cap\:\left(\mathrm{4}\right)\:\cap\:\left(\mathrm{5}\right)\:\cap\:\left(\mathrm{6}\right)\:=\:\mathrm{9}\:<\:{x}\:\leqslant\:\mathrm{21478} \\…

log-2-8x-log-3-27x-x-2-x-0-

Question Number 90434 by john santu last updated on 23/Apr/20 $$\frac{\mathrm{log}_{\mathrm{2}} \left(\mathrm{8}{x}\right).\mathrm{log}_{\mathrm{3}} \left(\mathrm{27}{x}\right)}{{x}^{\mathrm{2}} −\mid{x}\mid}\:\leqslant\:\mathrm{0}\: \\ $$ Commented by jagoll last updated on 28/Apr/20 $${how}\:\frac{\mathrm{1}}{\mathrm{8}}\:<\:\frac{\mathrm{1}}{\mathrm{27}}\:?\: \\…