Question Number 197419 by universe last updated on 16/Sep/23 Answered by cortano12 last updated on 17/Sep/23 $$\:\:\:\:\begin{cases}{\left(\mathrm{2a}\right)^{\mathrm{ln}\:\mathrm{a}} \:=\:\left(\mathrm{bc}\right)^{\mathrm{ln}\:\mathrm{b}} }\\{\mathrm{b}^{\mathrm{ln}\:\mathrm{2}} \:=\:\mathrm{a}^{\mathrm{ln}\:\mathrm{c}} \:}\end{cases} \\ $$$$\:\:\:\:\:\begin{cases}{\mathrm{ln}\:\left(\mathrm{2a}\right).\:\mathrm{ln}\:\left(\mathrm{a}\right)\:=\:\mathrm{ln}\:\left(\mathrm{b}\right).\:\mathrm{ln}\:\left(\mathrm{bc}\right)}\\{\mathrm{ln}\:\left(\mathrm{b}\right).\:\mathrm{ln}\:\left(\mathrm{2}\right)=\:\mathrm{ln}\:\left(\mathrm{c}\right).\:\mathrm{ln}\:\left(\mathrm{a}\right)}\end{cases} \\ $$$$\:\:\Rightarrow\mathrm{ln}\:\mathrm{a}\:\left\{\mathrm{ln}\:\mathrm{2}+\mathrm{ln}\:\mathrm{a}\right\}=\:\mathrm{ln}\:\mathrm{b}\:\left\{\mathrm{ln}\:\mathrm{b}+\mathrm{ln}\:\mathrm{c}\:\right\}…
Question Number 197409 by mathlove last updated on 16/Sep/23 Commented by mathlove last updated on 16/Sep/23 $${any}\:{solution}\:{is}\:{corect}\:{and}\: \\ $$$${any}\:{one}\:{is}\:{ancorect}\: \\ $$ Commented by AST last…
Question Number 197360 by hardmath last updated on 14/Sep/23 $$\mathrm{Find}: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{sin}^{\mathrm{2}} \:\left(\:\sqrt{\mathrm{x}}\:\right)\:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} \:\mathrm{dx}\:=\:? \\ $$ Answered by Mathspace last updated on 15/Sep/23…
Question Number 197312 by mathlove last updated on 13/Sep/23 $$\frac{\left({log}_{\mathrm{2}} \mathrm{20}\right)^{\mathrm{2}} −\left({log}_{\mathrm{2}} \mathrm{5}\right)^{\mathrm{2}} }{{log}_{\mathrm{2}} \mathrm{10}}=? \\ $$ Answered by som(math1967) last updated on 13/Sep/23 $$\mathrm{4}…
Question Number 197275 by uchihayahia last updated on 08/Oct/23 $$ \\ $$$$\:{how}\:{do}\:{i}\:{prove}\:{this},\:{help}\:{please}. \\ $$$$\:\mid\frac{{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}\mid\leqslant\frac{\mathrm{5}}{\mathrm{4}},\mid{x}\mid\leqslant\mathrm{2} \\ $$$$ \\ $$$$ \\ $$ Answered by AST…
Question Number 197297 by hardmath last updated on 12/Sep/23 $$\mathrm{677} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 197248 by hardmath last updated on 11/Sep/23 $$\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{R} \\ $$$$\frac{\mathrm{a}\:+\:\mathrm{2b}\:−\:\mathrm{3ac}}{\mathrm{3ac}}\:\:=\:\:\frac{\mathrm{a}\:+\:\mathrm{4b}\:−\:\mathrm{bc}}{\mathrm{b}} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{2b}}{\mathrm{a}}\:−\:\frac{\mathrm{3a}}{\mathrm{b}} \\ $$ Commented by Frix last updated on 11/Sep/23 $$−\frac{\left({c}+\mathrm{1}\right)\left(\mathrm{3}{c}^{\mathrm{2}} −\mathrm{15}{c}+\mathrm{1}\right)}{\mathrm{2}{c}}\pm\frac{\left({c}−\mathrm{1}\right)\sqrt{\mathrm{9}{c}^{\mathrm{4}}…
Question Number 197171 by MM42 last updated on 09/Sep/23 $$\mathrm{2}^{{log}_{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)} +\mathrm{2}×\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{log}_{\mathrm{3}} \mathrm{2}} \:=\mathrm{12} \\ $$$$\Rightarrow{x}=? \\ $$$$ \\ $$ Answered by Frix…
Question Number 197125 by Amidip last updated on 08/Sep/23 Commented by som(math1967) last updated on 08/Sep/23 $$\boldsymbol{{b}}=? \\ $$ Answered by Frix last updated on…
Question Number 197064 by Amidip last updated on 07/Sep/23 Answered by witcher3 last updated on 07/Sep/23 $$\mathrm{x}\sqrt{\mathrm{1}+\left(\frac{\mathrm{y}}{\mathrm{x}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} }+\mathrm{y}\left(\mathrm{1}+\left(\frac{\mathrm{y}}{\mathrm{x}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{a} \\ $$$$\mathrm{a}^{\mathrm{2}} =\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}}…