Question Number 115859 by bemath last updated on 29/Sep/20 $${Determine},\:{in}\:{simplest}\:{form}\:{the} \\ $$$${smallest}\:{of}\:{the}\:{three}\:{numbers}\:{x}, \\ $$$${y}\:{and}\:{z}\:{which}\:{satisfy}\:{the}\:{system} \\ $$$$\begin{cases}{\mathrm{log}\:_{\mathrm{9}} \left({x}\right)+\mathrm{log}\:_{\mathrm{9}} \left({y}\right)+\mathrm{log}\:_{\mathrm{3}} \left({z}\right)=\mathrm{2}}\\{\mathrm{log}\:_{\mathrm{16}} \left({x}\right)+\mathrm{log}\:_{\mathrm{4}} \left({y}\right)+\mathrm{log}\:_{\mathrm{16}} \left({z}\right)=\mathrm{1}}\\{\mathrm{log}\:_{\mathrm{5}} \left({x}\right)+\mathrm{log}\:_{\mathrm{25}} \left({y}\right)+\mathrm{log}\:_{\mathrm{25}} \left({z}\right)=\mathrm{0}}\end{cases}…
Question Number 50085 by F_Nongue last updated on 13/Dec/18 $$\mathrm{5}^{{x}+\mathrm{2}} −\mathrm{95}^{{x}} =\mathrm{2}^{{x}+\mathrm{9}} +\mathrm{1132}^{{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 181154 by mathlove last updated on 22/Nov/22 $$\left({log}_{\mathrm{15}} \mathrm{5}\right)^{\mathrm{2}} +\left({log}_{\mathrm{15}} \mathrm{3}\right)\left({log}_{\mathrm{15}} \mathrm{75}\right)=? \\ $$$$ \\ $$ Answered by SEKRET last updated on 22/Nov/22…
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 $${f}\left({x}−\mathrm{2}\right)={log}\left({x}−\mathrm{2}+\mathrm{2}\right)={logx} \\…
Question Number 115341 by bemath last updated on 25/Sep/20 $${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 $$\Rightarrow\mathrm{log}\:\left(\mathrm{tan}\:\mathrm{1}°×\mathrm{tan}\:\mathrm{2}°×\mathrm{tan}\:\mathrm{3}°×…×\mathrm{tan}\:\mathrm{89}°\right)={p} \\ $$$${consider}\:\mathrm{tan}\:\mathrm{89}°×\mathrm{tan}\:\mathrm{1}°=\mathrm{1}…
Question Number 115268 by bobhans last updated on 24/Sep/20 $$\sqrt{\mathrm{4}^{{x}} −\mathrm{5}.\mathrm{2}^{{x}+\mathrm{1}} +\mathrm{25}}\:+\sqrt{\mathrm{9}^{{x}} −\mathrm{2}.\mathrm{3}^{{x}+\mathrm{2}} +\mathrm{17}}\:\leqslant\:\mathrm{2}^{{x}} −\mathrm{5} \\ $$ Answered by john santu last updated on 24/Sep/20…
Question Number 115246 by bemath last updated on 24/Sep/20 $$\:\:\:\:\mathrm{5}^{\left({x}+\mathrm{1}\right)^{\mathrm{2}} } \:+\:\mathrm{625}\:\leqslant\:\mathrm{5}^{{x}^{\mathrm{2}} +\mathrm{2}} \:+\:\mathrm{5}^{\mathrm{2}{x}+\mathrm{3}} \\ $$ Commented by bobhans last updated on 24/Sep/20 $${let}\:\mathrm{5}^{{x}^{\mathrm{2}} }…
Question Number 115238 by bemath last updated on 24/Sep/20 $$\:\:\:\mathrm{64}^{{x}^{\mathrm{2}} −\frac{\mathrm{3}}{\mathrm{4}}{x}} \:\leqslant\:\left(\sqrt{\mathrm{8}}\right)^{{x}^{\mathrm{3}} } \: \\ $$ Answered by Rasheed.Sindhi last updated on 24/Sep/20 $$\mathrm{64}^{{x}^{\mathrm{2}} −\frac{\mathrm{3}}{\mathrm{4}}{x}}…
Question Number 49691 by Rio Michael last updated on 09/Dec/18 $${simplify}\:\frac{{log}_{\mathrm{3}} \mathrm{64}\:×\:{log}_{\mathrm{4}} \mathrm{243}}{{log}_{\mathrm{2}} \mathrm{16}} \\ $$ Answered by math1967 last updated on 09/Dec/18 $$\frac{{log}_{\mathrm{3}} \mathrm{4}^{\mathrm{3}}…
Question Number 180014 by cortano1 last updated on 06/Nov/22 $$\:\:\mathrm{Given}\:\mathrm{80}^{{a}} \:=\:\mathrm{5}\:\mathrm{and}\:\mathrm{80}^{{b}} \:=\:\mathrm{2} \\ $$$$\:\mathrm{then}\:\mathrm{25}^{\frac{\mathrm{1}−{a}−\mathrm{2}{b}}{\mathrm{1}+{a}−\mathrm{4}{b}}} \:=?\: \\ $$ Answered by srikanth2684 last updated on 06/Nov/22 $$\mathrm{25}^{\frac{\mathrm{ln}_{\mathrm{80}}…