Category: Logarithms

Question Number 100666 by bobhans last updated on 28/Jun/20 $$\mathrm{find}\mathrm{solution}\mathrm{set}\mathrm{of}\mathrm{inequality}$$$${(\log {}_{2}x-2)}^{3x-1}<{(\log {}_{2}x-2)}^{3-x}$$ Commented by Rasheed.Sindhi last updated on 28/Jun/20 $$\left(\mathrm{log}\:_{\mathrm{2}}…

Question Number 100151 by student work last updated on 25/Jun/20 $$\sqrt{\mathrm{lnx}}-\ln \sqrt{\mathrm{x}}=0\mathrm{x}=?$$ Commented by bobhans last updated on 25/Jun/20 $$\mathrm{set}\sqrt{\ln \left(\mathrm{x}\right)}=\mathrm{u}$$$$\mathrm{u}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{u}^{\mathrm{2}} \:=\mathrm{0}\:\Rightarrow\frac{\mathrm{1}}{\mathrm{2}}\mathrm{u}\left(\mathrm{2}−\mathrm{u}\right)=\mathrm{0} \…

Question Number 34301 by math1967 last updated on 03/May/18 $$If{log}_{12}18=a,find{log}_{24}16interm$$$$ofa$$ Answered by MJS last updated on 03/May/18 $$\mathrm{12}^{{a}} =\mathrm{18}…

Question Number 165178 by cortano1 last updated on 27/Jan/22 $$x\in R\Rightarrow \mid \log {}_2\left(\frac{x}{2}\right){\mid }^3+\mid \log {}_2\left(2x\right){\mid }^3=28$$ Answered by aleks041103 last updated on 27/Jan/22 $${log}_{\mathrm{2}} \left({x}/\mathrm{2}\right)={log}_{\mathrm{2}}…

Question Number 165068 by cortano1 last updated on 25/Jan/22 Commented by bobhans last updated on 25/Jan/22 $$\Rightarrow {\mathrm{x}}^{\log {}_{81}\left(243\right)}-2\mathrm{x}={(\mathrm{x}+2)}^{\log {}_{16}\left(2\right)}-8$$$$\Rightarrow\mathrm{x}^{\frac{\mathrm{5}}{\mathrm{4}}} −\mathrm{2x}\:=\:\left(\mathrm{x}+\mathrm{2}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} −\mathrm{8}…