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Question Number 197147 by sonukgindia last updated on 08/Sep/23

Answered by Frix last updated on 10/Sep/23

$$\mathrm{Obviously}x=1\vee x=\frac{\pi }{2}\vee x=\frac{5\pi }{2}\mathrm{because}$$$$\ln 1=0\mathrm{and}\sin \frac{\pi }{2}=1$$

Commented by sonukgindia last updated on 09/Sep/23

$$o$$$$thinkallpossibilities$$

Answered by MM42 last updated on 09/Sep/23

$$a=x^{ln\left(sinx\right)}\Rightarrow lna=lnx\times lnsinx\left(i\right)$$$$b={\left(sinx\right)}^{lnx}\Rightarrow lnb=lnx\times lnsinx\left(ii\right)$$$$\left(i\right)=\left(ii\right)\Rightarrow a=b\Rightarrow 4a=4\Rightarrow a=1$$$$\Rightarrow lnx\times lnsinx=0$$$$\Rightarrow lnx=0\Rightarrow \overline{)\begin{array}{c}x=1\end{array}}✓orlnsinx=0$$$$\Rightarrow sinx=1\Rightarrow \overline{)\begin{array}{c}x=2k\pi +\frac{\pi }{2}\end{array}}✓$$$$$$

Commented by MM42 last updated on 09/Sep/23

Commented by MathematicalUser2357 last updated on 10/Sep/23

$${\mathrm{That}}^{\prime }\mathrm{s}\mathrm{Desmos}$$

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