Question Number 191155 by mathlove last updated on 19/Apr/23 Answered by mahdipoor last updated on 19/Apr/23 $${log}\left({xy}\right)={log}\left({x}\right)+{log}\left({y}\right)\Rightarrow{x}={a}\:,\:{y}=\mathrm{1}+\frac{{b}}{{a}}\:\Rightarrow \\ $$$${log}\left({a}+{b}\right)={log}\left({a}\right)+{log}\left(\mathrm{1}+{b}/{a}\right) \\ $$$$…….. \\ $$$${b}=\mathrm{10}^{{B}} \:,\:{a}=\mathrm{10}^{{A}} \:,\:{c}=\mathrm{10}^{{C}}…
Question Number 59401 by Pranay last updated on 09/May/19 $$\mathrm{5}{log}_{\mathrm{4}\sqrt{\mathrm{2}}} \left(\mathrm{3}−\sqrt{\mathrm{6}}\:\right)\:−\mathrm{6}{log}_{\mathrm{8}} \left(\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}\right) \\ $$ Answered by prakash jain last updated on 10/May/19 $$\mathrm{4}\sqrt{\mathrm{2}}=\left(\sqrt{\mathrm{2}}\right)^{\mathrm{5}} \\ $$$$\mathrm{8}=\left(\sqrt{\mathrm{2}}\right)^{\mathrm{6}}…
Question Number 124880 by WilliamsErinfolami last updated on 06/Dec/20 $${Solve}\:{for}\:{x} \\ $$$${x}^{{log}_{\mathrm{5}} \mathrm{3}{x}} =\mathrm{12}{x} \\ $$ Answered by mr W last updated on 06/Dec/20 $$\left(\mathrm{log}_{\mathrm{5}}…
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Question Number 59147 by Pranay last updated on 05/May/19 $$\underset{\mathrm{1}°} {\overset{\mathrm{89}°} {\sum}}\:{log}_{\mathrm{2}} {tan}\:{r}° \\ $$ Answered by ajfour last updated on 05/May/19 $$=\mathrm{log}\:_{\mathrm{2}} \mathrm{1}=\mathrm{0}\:. \\…
Question Number 188752 by Soma last updated on 06/Mar/23 Commented by Yacouba last updated on 06/Mar/23 $$\mathrm{D}{f}=\:\left\{{x}\in\mathbb{R}/{x}>\mathrm{0}\:{et}\:\mathrm{ln}{x}\neq\mathrm{0}\right\} \\ $$ Answered by a.lgnaoui last updated on…
Question Number 121876 by oustmuchiya@gmail.com last updated on 12/Nov/20 Commented by liberty last updated on 12/Nov/20 $$\Rightarrow\:\sqrt{\mathrm{x}−\mathrm{6}}\:=\:\mathrm{7}−\sqrt{\mathrm{x}−\mathrm{1}} \\ $$$$\Rightarrow\mathrm{x}−\mathrm{6}\:=\:\mathrm{49}−\mathrm{14}\sqrt{\mathrm{x}−\mathrm{1}}\:+\:\mathrm{x}−\mathrm{1}\: \\ $$$$\Rightarrow\mathrm{14}\sqrt{\mathrm{x}−\mathrm{1}}\:=\:\mathrm{54}\:\Rightarrow\sqrt{\mathrm{x}−\mathrm{1}}\:=\:\frac{\mathrm{27}}{\mathrm{7}} \\ $$$$\Rightarrow\mathrm{x}−\mathrm{1}\:=\:\frac{\mathrm{27}^{\mathrm{2}} }{\mathrm{49}}\:;\:\mathrm{x}\:=\:\frac{\mathrm{27}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}}…
Question Number 187406 by Fridunatjan08 last updated on 16/Feb/23 $$\mathrm{3}^{{x}} .\mathrm{8}^{\frac{{x}}{{x}+\mathrm{2}}} =\mathrm{6}{ln}\mathrm{0}−{log}\mathrm{10} \\ $$ Commented by Fridunatjan08 last updated on 16/Feb/23 $${can}\:{someone}\:{please}\:{help}\:{me}? \\ $$ Commented…
Question Number 121783 by Ar Brandon last updated on 11/Nov/20 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integer}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{satisfying}\: \\ $$$$\mathrm{the}\:\mathrm{inequality}\:\mathrm{2x}+\mathrm{1}<\mathrm{2log}_{\mathrm{2}} \left(\mathrm{x}+\mathrm{3}\right)\:\mathrm{is}\:\_\_\_. \\ $$ Answered by TANMAY PANACEA last updated on 11/Nov/20 $$…
Question Number 121778 by Ar Brandon last updated on 11/Nov/20 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integers}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{inequality} \\ $$$$\mathrm{3}^{\left(\mathrm{5}/\mathrm{2}\right)\mathrm{log}_{\mathrm{3}} \left(\mathrm{12}−\mathrm{3x}\right)} −\mathrm{3}^{\mathrm{log}_{\mathrm{2}} \mathrm{x}} >\mathrm{83}\:\mathrm{is}\:\_\_\_\_\: \\ $$ Commented by 676597498 last updated on…