Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 184019 by HeferH last updated on 02/Jan/23

 { ((y^x = 64)),((y^((x + 1)/(x − 1))  = 16)) :}   find “x”

$$\begin{cases}{{y}^{{x}} =\:\mathrm{64}}\\{{y}^{\frac{{x}\:+\:\mathrm{1}}{{x}\:−\:\mathrm{1}}} \:=\:\mathrm{16}}\end{cases} \\ $$$$\:{find}\:``{x}'' \\ $$

Commented by a.lgnaoui last updated on 02/Jan/23

Hapy New year

$${Hapy}\:{New}\:{year} \\ $$

Commented by Gazella thomsonii last updated on 02/Jan/23

=Ha^2 e^2 p^2 wy^2 r

$$=\mathrm{Ha}^{\mathrm{2}} \mathrm{e}^{\mathrm{2}} \mathrm{p}^{\mathrm{2}} \mathrm{wy}^{\mathrm{2}} \mathrm{r} \\ $$

Answered by manolex last updated on 02/Jan/23

xlny=3ln4  ((x+1)/(x−1))lny=2ln4  x=((3(x+1))/(2(x−1)))  2x^2 −2x=3x+3  2x^2 −5x−3=0  2x               +1  x                  −3  2x+1=0     x=−(1/2)  x−3=0       x=3  comprobando  x_1 =3     x_2 =−(1/2)

$${xlny}=\mathrm{3}{ln}\mathrm{4} \\ $$$$\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}{lny}=\mathrm{2}{ln}\mathrm{4} \\ $$$${x}=\frac{\mathrm{3}\left({x}+\mathrm{1}\right)}{\mathrm{2}\left({x}−\mathrm{1}\right)} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{x}=\mathrm{3}{x}+\mathrm{3} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}−\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{2}{x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\mathrm{1} \\ $$$${x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\mathrm{3} \\ $$$$\mathrm{2}{x}+\mathrm{1}=\mathrm{0}\:\:\:\:\:{x}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${x}−\mathrm{3}=\mathrm{0}\:\:\:\:\:\:\:{x}=\mathrm{3} \\ $$$${comprobando} \\ $$$${x}_{\mathrm{1}} =\mathrm{3}\:\:\:\:\:{x}_{\mathrm{2}} =−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$

Commented by manolex last updated on 02/Jan/23

Happy new year,Sr.HeferH

$${Happy}\:{new}\:{year},{Sr}.{HeferH} \\ $$

Commented by HeferH last updated on 02/Jan/23

Happy new year !   :)

$${Happy}\:{new}\:{year}\:! \\ $$$$\left.\::\right) \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com