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Category: Logarithms

Question-100720

Question Number 100720 by bemath last updated on 28/Jun/20 Commented by 1549442205 last updated on 28/Jun/20 $$ \\ $$$$\mathrm{one}\:\mathrm{other}\:\mathrm{way}:\mathrm{the}\:\mathrm{conditions}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{inequality}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{as}:\frac{\mathrm{x}−\mathrm{5}}{\mathrm{5}}>\mathrm{0}\Leftrightarrow\mathrm{x}>\mathrm{5} \\ $$$$\mathrm{Since}\:\mathrm{log}_{\mathrm{8}} \frac{\mathrm{x}−\mathrm{5}}{\mathrm{5}}=\mathrm{log}_{\mathrm{2}} \left(\frac{\mathrm{x}−\mathrm{5}}{\mathrm{5}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}}…

If-log-2x-1-18-log-18-1-3y-log-3y-1-2x-find-3x-2y-

Question Number 100675 by bobhans last updated on 28/Jun/20 $$\mathrm{If}\:\mathrm{log}\:_{\mathrm{2x}} \left(\frac{\mathrm{1}}{\mathrm{18}}\right)\:=\:\mathrm{log}\:_{\mathrm{18}} \left(\frac{\mathrm{1}}{\mathrm{3y}}\right)\:=\:\mathrm{log}\:_{\mathrm{3y}} \left(\frac{\mathrm{1}}{\mathrm{2x}}\right) \\ $$$$\mathrm{find}\:\mathrm{3x}−\mathrm{2y}\: \\ $$ Commented by bramlex last updated on 28/Jun/20 $$\Leftrightarrow\:\mathrm{2}{x}\:=\:\mathrm{3}{y}\:=\:\mathrm{18}\:\rightarrow\begin{cases}{{x}=\mathrm{9}}\\{{y}=\mathrm{6}}\end{cases}…

find-solution-set-of-inequality-log-2-x-2-3x-1-lt-log-2-x-2-3-x-

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

A-uniform-sphere-of-weight-W-rest-between-a-smooth-vertical-plane-and-a-smooth-plane-inclined-at-an-angle-with-the-vertical-plane-Find-the-reaction-at-the-contact-surfaces-

Question Number 165818 by MikeH last updated on 08/Feb/22 $$\mathrm{A}\:\mathrm{uniform}\:\mathrm{sphere}\:\mathrm{of}\:\mathrm{weight}\:{W} \\ $$$$\mathrm{rest}\:\mathrm{between}\:\mathrm{a}\:\mathrm{smooth}\:\:\mathrm{vertical} \\ $$$$\mathrm{plane}\:\mathrm{and}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{plane}\:\mathrm{inclined} \\ $$$$\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:\mathrm{vertical} \\ $$$$\mathrm{plane}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{reaction}\:\mathrm{at}\:\mathrm{the}\: \\ $$$$\mathrm{contact}\:\mathrm{surfaces}.\: \\ $$ Answered by ajfour…

lnx-ln-x-0-x-

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