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Category: Logarithms

Question-208139

Question Number 208139 by efronzo1 last updated on 06/Jun/24 $$\:\:\:\: \\ $$ Answered by Ghisom last updated on 06/Jun/24 $${x}>\mathrm{0} \\ $$$$\frac{\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:+\mathrm{ln}\:{x}}{\mathrm{ln}\:\mathrm{5}\:+\mathrm{ln}\:\mathrm{2}}=\frac{\mathrm{ln}\:{x}}{\mathrm{ln}\:\mathrm{2}} \\ $$$$\frac{\mathrm{ln}\:\left({x}^{\mathrm{2}}…

Question-205496

Question Number 205496 by cortano12 last updated on 22/Mar/24 Answered by Frix last updated on 22/Mar/24 $${x}>\mathrm{0} \\ $$$${t}=\sqrt[{\mathrm{3}}]{{x}} \\ $$$$\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{1}+{t}\right)\:=\mathrm{3log}_{\mathrm{7}} \:{x} \\ $$$$\mathrm{Obviously}\:{t}=\mathrm{7}…

Question-204174

Question Number 204174 by patrice last updated on 08/Feb/24 Answered by Faetmaaa last updated on 27/Feb/24 $$\left.\mathrm{3}\right)- \\ $$$$\forall{n}\in\boldsymbol{\mathrm{N}}^{\bigstar} \\ $$$${S}_{{n}} \:=\:\frac{\mathrm{1}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{ln}\left(\frac{{k}}{{n}}\right) \\…

valeur-x-ECA-90-

Question Number 203375 by a.lgnaoui last updated on 17/Jan/24 $$\:\mathrm{valeur}\:\boldsymbol{\mathrm{x}}? \\ $$$$\left(\measuredangle\mathrm{ECA}\:\:=\mathrm{90}\right) \\ $$ Commented by mr W last updated on 18/Jan/24 $$\mathrm{17}\:\mathrm{sin}\:\mathrm{5}{x}+\mathrm{17}\:\mathrm{cos}\:\mathrm{5}{x}\:\mathrm{tan}\:{x}=\mathrm{13} \\ $$$$\mathrm{sin}\:\mathrm{5}{x}+\mathrm{cos}\:\mathrm{5}{x}\:\mathrm{tan}\:{x}=\frac{\mathrm{13}}{\mathrm{17}}…

If-log-12-18-A-and-log-24-54-B-then-prove-that-AB-5-A-B-1-

Question Number 202172 by MATHEMATICSAM last updated on 22/Dec/23 $$\mathrm{If}\:\mathrm{log}_{\mathrm{12}} \mathrm{18}\:=\:\mathrm{A}\:\mathrm{and}\:\mathrm{log}_{\mathrm{24}} \mathrm{54}\:=\:\mathrm{B}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{AB}\:+\:\mathrm{5}\left(\mathrm{A}\:−\:\mathrm{B}\right)\:=\:\mathrm{1}. \\ $$ Answered by Rasheed.Sindhi last updated on 22/Dec/23 $$\mathrm{12}^{\mathrm{A}} =\mathrm{18}\:\&\:\mathrm{24}^{\mathrm{B}}…