Question Number 34301 by math1967 last updated on 03/May/18 $${If}\:{log}_{\mathrm{12}} \mathrm{18}={a}\:,{find}\:{log}_{\mathrm{24}} \mathrm{16}\:{in}\:{term} \\ $$$${of}\:\:{a} \\ $$ Answered by MJS last updated on 03/May/18 $$\mathrm{12}^{{a}} =\mathrm{18}…
Question Number 99681 by Algoritm last updated on 22/Jun/20 Answered by floor(10²Eta[1]) last updated on 22/Jun/20 $$\mathrm{1}−\mathrm{2}{x}>\mathrm{0}\Rightarrow{x}<\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{1}−\mathrm{2}{x}\neq\mathrm{1}\Rightarrow{x}\neq\mathrm{0} \\ $$$${but}\:{we}\:{know}\:{that}\:{for}\:{all}\:{x}<\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${x}−\mathrm{2018}\:{will}\:{be}\:{negative},\:{so}\:{for}\:{that} \\ $$$${expression}\:{be}\:{positive}…
Question Number 165178 by cortano1 last updated on 27/Jan/22 $$\:\:{x}\in{R}\:\Rightarrow\:\mid\:\mathrm{log}\:_{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)\mid^{\mathrm{3}} +\mid\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{2}{x}\right)\mid^{\mathrm{3}} =\mathrm{28} \\ $$ Answered by aleks041103 last updated on 27/Jan/22 $${log}_{\mathrm{2}} \left({x}/\mathrm{2}\right)={log}_{\mathrm{2}}…
Question Number 165136 by saboorhalimi last updated on 26/Jan/22 Answered by MJS_new last updated on 26/Jan/22 $$\mathrm{obviously}\:{a}=\mathrm{8} \\ $$$$\mathrm{log}_{\mathrm{3}} \:\mathrm{9}\:=\mathrm{log}_{\mathrm{4}} \:\mathrm{16}\:=\mathrm{2} \\ $$ Commented by…
Question Number 165068 by cortano1 last updated on 25/Jan/22 Commented by bobhans last updated on 25/Jan/22 $$\:\Rightarrow\mathrm{x}^{\mathrm{log}\:_{\mathrm{81}} \left(\mathrm{243}\right)} −\mathrm{2x}\:=\:\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{log}\:_{\mathrm{16}} \left(\mathrm{2}\right)} −\mathrm{8} \\ $$$$\Rightarrow\mathrm{x}^{\frac{\mathrm{5}}{\mathrm{4}}} −\mathrm{2x}\:=\:\left(\mathrm{x}+\mathrm{2}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} −\mathrm{8}…
Question Number 164985 by cortano1 last updated on 24/Jan/22 Answered by Eulerian last updated on 24/Jan/22 $$\: \\ $$$$\:\boldsymbol{\mathrm{Solution}}: \\ $$$$\:\mathrm{3}\centerdot\frac{\mathrm{log}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{log}^{\mathrm{2}} \left(\mathrm{2}\right)}\:−\:\mathrm{1}\:−\:\mathrm{9}\centerdot\frac{\mathrm{log}^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{log}^{\mathrm{2}} \left(\mathrm{x}\right)}\:=\:\mathrm{25}…
Question Number 164806 by saboorhalimi last updated on 22/Jan/22 Commented by cortano1 last updated on 22/Jan/22 $$\:\mathrm{log}\:_{\mathrm{12}} \left(\mathrm{3}\right)={a}\:\Rightarrow\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{12}\right)=\frac{\mathrm{1}}{{a}} \\ $$$$\Rightarrow\mathrm{1}+\mathrm{2}\:\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2}\right)=\frac{\mathrm{1}}{{a}}\: \\ $$$$\Rightarrow\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2}\right)=\:\frac{\mathrm{1}−{a}}{\mathrm{2}{a}}\:…
Question Number 99050 by bemath last updated on 18/Jun/20 $$\mathrm{5}^{\mathrm{5}−\mathrm{3}{x}} \:+\:\mathrm{2}^{{x}+\mathrm{5}} \:=\:\mathrm{5}^{\mathrm{7}−\mathrm{3}{x}} \:−\mathrm{2}^{{x}+\mathrm{6}} \: \\ $$ Commented by bobhans last updated on 18/Jun/20 $$\frac{\mathrm{5}^{\mathrm{5}} }{\mathrm{5}^{\mathrm{3x}}…
Question Number 32885 by scientist last updated on 05/Apr/18 Answered by MJS last updated on 05/Apr/18 $$\mathrm{log}\:{u}={a} \\ $$$$\mathrm{log}\:{v}={b} \\ $$$$\mathrm{log}\:{s}={c} \\ $$$$\mathrm{log}\:{t}={d} \\ $$$$\mathrm{all}\:\mathrm{we}\:\mathrm{need}\:\mathrm{is}\:\mathrm{log}\:\frac{{p}}{{q}}=\mathrm{log}\:{p}−\mathrm{log}\:{q}…
Question Number 97725 by john santu last updated on 09/Jun/20 $$\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{4x}\right)=\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{x}\right) \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$ Commented by prakash jain last updated on 09/Jun/20…