Question Number 179722 by Acem last updated on 01/Nov/22 $$\mathrm{1000}^{\mathrm{500}\:{x}} \:=\:\sqrt{\mathrm{200}} \\ $$ Commented by CElcedricjunior last updated on 02/Nov/22 $$\mathrm{1000}^{\mathrm{500}\boldsymbol{\mathrm{x}}} =\sqrt{\mathrm{200}} \\ $$$$\mathrm{500}\boldsymbol{\mathrm{xln}}\mathrm{10}^{\mathrm{3}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\boldsymbol{\mathrm{ln}}\mathrm{2}+\boldsymbol{\mathrm{ln}}\mathrm{100}\right)…
Question Number 179679 by ROOSEVELT last updated on 01/Nov/22 $$\int_{\mathrm{2}} ^{\mathrm{4}} \mathrm{tan}\:\left({x}\right) \\ $$ Answered by Acem last updated on 01/Nov/22 $${a}=\:−\mathrm{ln}\:\mid\mathrm{cos}\:{x}\mid\:\mid_{\mathrm{2}} ^{\mathrm{4}} \:=\:−\mathrm{ln}\:\mid\mathrm{cos}\:\mathrm{4}\mid+\:\mathrm{ln}\:\mid\mathrm{cos}\:\mathrm{2}\mid \\…
Question Number 113872 by Aina Samuel Temidayo last updated on 15/Sep/20 $$\mathrm{log}_{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}} \mathrm{sinx}\:>\mathrm{0},\:\mathrm{x}\in\left[\mathrm{0},\mathrm{4}\pi\right],\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{which}\:\mathrm{are} \\ $$$$\mathrm{integral}\:\mathrm{multiples}\:\mathrm{of}\:\frac{\pi}{\mathrm{4}},\:\mathrm{is}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 113862 by Aina Samuel Temidayo last updated on 15/Sep/20 Answered by 1549442205PVT last updated on 16/Sep/20 $$\mathrm{From}\:\mathrm{the}\:\mathrm{hypotesis}\:\mathrm{we}\:\mathrm{have} \\ $$$$\frac{\mathrm{logx}}{\mathrm{b}−\mathrm{c}}=\frac{\mathrm{logy}}{\mathrm{c}−\mathrm{a}}=\frac{\mathrm{logz}}{\mathrm{a}−\mathrm{b}}=\mathrm{k}.\mathrm{Hence},\mathrm{we}\:\mathrm{get} \\ $$$$\begin{cases}{\mathrm{logx}=\mathrm{k}\left(\mathrm{b}−\mathrm{c}\right)}\\{\mathrm{logy}=\mathrm{k}\left(\mathrm{c}−\mathrm{a}\right)}\\{\mathrm{logz}=\mathrm{k}\left(\mathrm{a}−\mathrm{b}\right)}\end{cases} \\ $$$$\mathrm{Adding}\:\mathrm{up}\:\mathrm{three}\:\mathrm{equalities}\:\mathrm{we}\:\mathrm{obtain}…
Question Number 113811 by Aina Samuel Temidayo last updated on 15/Sep/20 $$\mathrm{If}\:\mathrm{log}_{\mathrm{12}} \mathrm{27}=\mathrm{a},\:\mathrm{express}\:\mathrm{log}_{\mathrm{6}} \mathrm{16}\:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{a}. \\ $$ Answered by bemath last updated on 15/Sep/20…
Question Number 113800 by Aina Samuel Temidayo last updated on 15/Sep/20 $$\mathrm{log}\:\left(\mathrm{ab}\right)−\mathrm{log}\mid\mathrm{b}\mid\:= \\ $$$$ \\ $$$$\mathrm{A}.\:\mathrm{log}\left(\mathrm{a}\right)\:\mathrm{B}.\:\mathrm{log}\:\mid\mathrm{a}\mid\:\mathrm{C}.\:−\mathrm{log}\left(\mathrm{a}\right)\:\mathrm{D}. \\ $$$$\mathrm{None}\:\mathrm{of}\:\mathrm{these}. \\ $$ Answered by MJS_new last updated…
Question Number 113803 by Aina Samuel Temidayo last updated on 15/Sep/20 $$\mathrm{If}\:\mathrm{a}=\mathrm{log}_{\mathrm{24}} \mathrm{12},\:\mathrm{b}=\mathrm{log}_{\mathrm{36}} \mathrm{24}\:\mathrm{and} \\ $$$$\mathrm{c}=\mathrm{log}_{\mathrm{48}} \mathrm{36},\:\mathrm{then}\:\mathrm{1}+\mathrm{abc}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$ \\ $$$$\left(\mathrm{A}\right)\:\mathrm{2ab}\:\left(\mathrm{B}\right)\:\mathrm{2ac}\:\left(\mathrm{C}\right)\:\mathrm{2bc}\:\left(\mathrm{D}\right)\:\mathrm{0} \\ $$ Answered by…
Question Number 48202 by F_Nongue last updated on 20/Nov/18 $${how}\:{can}\:{I}\:{get}\:{the}\:{x}? \\ $$$$\left.{a}\right)\mathrm{3}^{{x}} +\mathrm{4}^{{x}} =\mathrm{5}^{{x}} \\ $$$$\left.{b}\right)\mathrm{7}^{\mathrm{6}−{x}} ={x}+\mathrm{2} \\ $$$$\left.{c}\right)\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\right)^{{x}} +\left(\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\right)^{{x}} =\mathrm{2}^{{x}} \\ $$$$\left.{d}\right)\mathrm{3}^{{x}−\mathrm{2}} =\frac{\mathrm{9}}{{x}} \\…
Question Number 113426 by bemath last updated on 13/Sep/20 Answered by bemath last updated on 13/Sep/20 $$\left(\mathrm{1}\right)\:\mathrm{3}^{\mathrm{3}{b}} \:=\:\mathrm{5}^{\mathrm{4}{a}} \:\rightarrow\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{3}^{\mathrm{3}{b}} \right)=\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{5}^{\mathrm{4}{a}} \right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{3}^{\mathrm{2}{b}+\mathrm{2}}…
Question Number 112808 by Aina Samuel Temidayo last updated on 09/Sep/20 Answered by 1549442205PVT last updated on 10/Sep/20 $$\mathrm{We}\:\mathrm{have}\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{10}+\mathrm{2x}\right)=\mathrm{log}_{\mathrm{10}} \left(\mathrm{x}−\mathrm{4}\right)+\mathrm{2} \\ $$$$\Leftrightarrow\left[\mathrm{log}_{\mathrm{2}} \left(\mathrm{10}+\mathrm{2x}\right)−\mathrm{2}\right]−\mathrm{log}_{\mathrm{10}} \left(\mathrm{x}−\mathrm{4}\right)=\mathrm{0}\left(\mathrm{1}\right)…