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 204647 by Engr_Jidda last updated on 24/Feb/24

Answered by Rasheed.Sindhi last updated on 24/Feb/24

$${\left(\frac{x}{2}\right)}^{\frac{x}{2}-1}=3^2$$$$\Leftarrow \frac{x}{2}=3\wedge \frac{x}{2}-1=2\Rightarrow x=6$$

Commented by Engr_Jidda last updated on 24/Feb/24

$$thanks$$

Answered by Rasheed.Sindhi last updated on 24/Feb/24

$$\frac{{\left(\frac{x}{2}\right)}^{\frac{x}{2}}}{\frac{x}{2}}=9=\frac{3^3}{3}$$$$\frac{x}{2}=3\Rightarrow x=6$$

Commented by Frix last updated on 24/Feb/24

$${\mathrm{There}}^{\prime }\mathrm{s}\mathrm{a}{2}^{\mathrm{nd}}\mathrm{solution}\mathrm{we}\mathrm{can}\mathrm{only}$$$$\mathrm{approximste}:$$$$x\approx .179044868$$

Commented by Frix last updated on 24/Feb/24

$$\mathrm{With}x=2t\mathrm{we}\mathrm{get}$$$$t^{t-1}=9$$$$(t-1)\ln t=2\ln 3$$$$\mathrm{Obviously}t=3$$$$0<t<1\Rightarrow t-1<0\wedge \ln t<0\Rightarrow \mathrm{lhs}>0$$$$\Rightarrow {\mathrm{there}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{solution}\mathrm{in}\mathrm{this}\mathrm{interval}$$

Answered by bello6646 last updated on 24/Feb/24

$$\mathbf{solution}$$$$$$$$9=3^{3-1}$$$${\left(\frac{\mathbf{x}}{2}\right)}^{\frac{\mathbf{x}}{2}-1}=3^{3-1}$$$$$$$$\Rightarrow \frac{\mathbf{x}}{2}=3\Rightarrow \mathbf{x}=6$$

Answered by lepuissantcedricjunior last updated on 26/Feb/24

$${\left(\frac{\mathbf{x}}{2}\right)}^{\frac{\mathbf{x}}{2}-1}=9=3^2$$$$\frac{\mathbf{x}}{2}\mathbf{ln}\left(\frac{\mathbf{x}}{2}\right)-\mathbf{ln}\left(\frac{\mathbf{x}}{2}\right)=2\mathbf{ln}3=\frac{6}{2}\mathbf{ln}\left(\frac{6}{2}\right)-\mathbf{ln}\left(\frac{6}{2}\right))$$$$=>\frac{\mathbf{x}}{2}=\frac{6}{2}\mathbf{par}\mathbf{identif}=>\underbrace{\mathbf{x}=6}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com