Category: Logarithms

Question Number 5592 by Rasheed Soomro last updated on 21/May/16 $$\mathrm{Find}\mathrm{the}\mathrm{positive}\mathrm{values}\mathrm{of}\mathrm{x}\mathrm{for}$$$$\mathrm{which}{9\mathrm{x}}^{\frac{2}{3}}+{4\mathrm{x}}^{-\frac{2}{3}}=37.$$ Answered by prakash jain last updated on 21/May/16…

Question Number 5579 by Rasheed Soomro last updated on 21/May/16 $$\mathrm{Without}\mathrm{using}\mathrm{a}\mathrm{calculator},\mathrm{evaluate}$$$${\left(\log 5\right)}^2+\log 2\log 50$$ Answered by FilupSmith last updated on 21/May/16 $$\mathrm{log}\:{x}\:=\:\mathrm{log}_{\mathrm{10}} {x}…

Question Number 71016 by mr W last updated on 10/Oct/19 $$\mathbf{ln}(\mathit{e}+\mathbf{ln}(\mathit{e}+\mathbf{ln}(\mathit{e}+\dots )))=?$$ Answered by mr W last updated on 11/Oct/19 $$\mathbf{ln}(\mathit{e}+\mathbf{ln}(\mathit{e}+\mathbf{ln}(\mathit{e}+\dots )))=x$$$$\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+{x}\right)={x} \…

Question Number 136256 by EDWIN88 last updated on 20/Mar/21 $$\log {}_{(\mathrm{x}-2)}(10-3\mathrm{x})<2$$ Answered by liberty last updated on 20/Mar/21 $$\left(1\right)10-3x>0;3x-10<0$$$$x<\frac{10}{3}$$$$\left(\mathrm{2}\right)\:\mathrm{log}\:_{\left({x}−\mathrm{2}\right)}…

Question Number 5039 by Rasheed Soomro last updated on 05/Apr/16 $${\log }_{\left(\frac{\mathrm{x}}{\mathrm{y}}\right)}\left(\frac{\mathrm{y}}{\mathrm{x}}\right)=?$$ Answered by LMTV last updated on 05/Apr/16 $${\left(\frac{x}{y}\right)}^{?}=\frac{y}{x}$$$$?=−\mathrm{1}…