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Category: Logarithms

0-16-log-2-5-1-3-1-3-2-1-3-3-

Question Number 116491 by bemath last updated on 04/Oct/20 $$\left(\mathrm{0}.\mathrm{16}\right)^{\mathrm{log}\:_{\mathrm{2}.\mathrm{5}} \left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }+…\right)} \:=? \\ $$ Answered by bobhans last updated on 04/Oct/20 $$\mathrm{Only}\:\mathrm{applying}\:\mathrm{property}\:\mathrm{of}\:\mathrm{logarithm} \\…

6-log-3-2-1-3-2-4-1-3-2-4-1-3-2-4-1-3-2-

Question Number 116085 by Ar Brandon last updated on 30/Sep/20 $$\mathrm{6}+\mathrm{log}_{\frac{\mathrm{3}}{\mathrm{2}}} \left\{\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\centerdot\centerdot\centerdot}}}\right\}=\:? \\ $$ Commented by Dwaipayan Shikari last updated on 30/Sep/20 $$\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}….}}=\mathrm{a} \\ $$$$\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\mathrm{a}=\mathrm{a}^{\mathrm{2}}…

Determine-in-simplest-form-the-smallest-of-the-three-numbers-x-y-and-z-which-satisfy-the-system-log-9-x-log-9-y-log-3-z-2-log-16-x-log-4-y-log-16-z-1-log-5-x-lo

Question Number 115859 by bemath last updated on 29/Sep/20 $${Determine},\:{in}\:{simplest}\:{form}\:{the} \\ $$$${smallest}\:{of}\:{the}\:{three}\:{numbers}\:{x}, \\ $$$${y}\:{and}\:{z}\:{which}\:{satisfy}\:{the}\:{system} \\ $$$$\begin{cases}{\mathrm{log}\:_{\mathrm{9}} \left({x}\right)+\mathrm{log}\:_{\mathrm{9}} \left({y}\right)+\mathrm{log}\:_{\mathrm{3}} \left({z}\right)=\mathrm{2}}\\{\mathrm{log}\:_{\mathrm{16}} \left({x}\right)+\mathrm{log}\:_{\mathrm{4}} \left({y}\right)+\mathrm{log}\:_{\mathrm{16}} \left({z}\right)=\mathrm{1}}\\{\mathrm{log}\:_{\mathrm{5}} \left({x}\right)+\mathrm{log}\:_{\mathrm{25}} \left({y}\right)+\mathrm{log}\:_{\mathrm{25}} \left({z}\right)=\mathrm{0}}\end{cases}…

a-if-f-x-log-x-2-solve-the-equation-2-f-x-2-2-f-2x-2-4-logf-x-

Question Number 50080 by F_Nongue last updated on 13/Dec/18 $$\left.{a}\right)\:{if}\:{f}\left({x}\right)={log}\left({x}+\mathrm{2}\right),\:{solve}\:{the}\:{equation}: \\ $$$$\mathrm{2}^{{f}\left({x}−\mathrm{2}\right)} ×\mathrm{2}^{{f}\left(\mathrm{2}{x}+\mathrm{2}\right)} =\mathrm{4}^{{logf}\left({x}\right)} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 13/Dec/18 $${f}\left({x}−\mathrm{2}\right)={log}\left({x}−\mathrm{2}+\mathrm{2}\right)={logx} \\…

If-log-tan-1-log-tan-2-log-tan-3-log-tan-89-p-then-p-2-3-

Question Number 115341 by bemath last updated on 25/Sep/20 $${If}\:\mathrm{log}\:\mathrm{tan}\:\mathrm{1}°+\mathrm{log}\:\mathrm{tan}\:\mathrm{2}°+\mathrm{log}\:\mathrm{tan}\:\mathrm{3}°+…+\mathrm{log}\:\mathrm{tan}\:\mathrm{89}°={p} \\ $$$${then}\:{p}^{\mathrm{2}} +\mathrm{3}\:=\: \\ $$ Answered by bobhans last updated on 25/Sep/20 $$\Rightarrow\mathrm{log}\:\left(\mathrm{tan}\:\mathrm{1}°×\mathrm{tan}\:\mathrm{2}°×\mathrm{tan}\:\mathrm{3}°×…×\mathrm{tan}\:\mathrm{89}°\right)={p} \\ $$$${consider}\:\mathrm{tan}\:\mathrm{89}°×\mathrm{tan}\:\mathrm{1}°=\mathrm{1}…