(ax)^x=108 କୁ ସମାଧାନ କରନ୍ତୁ

$$( a x ) ^ { x } = 108$$

a ପାଇଁ ସମାଧାନ କରନ୍ତୁ (ଜଟଳି ସମାଧାନ)

$$a=\frac{e^{-\frac{2\pi n_{1}\left(Im(x)+iRe(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\times 108^{\frac{Re(x)-iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}}{x}$$

$$n_{1}\in \mathrm{Z}$$

$$xe^{\frac{2\pi n_{1}\left(Im(x)+iRe(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\neq 0$$

$$\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}\neq 0$$

a ପାଇଁ ସମାଧାନ କରନ୍ତୁ

$$\left\{\begin{matrix}a=-\frac{108^{\frac{1}{x}}}{x}\text{, }&x\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\\a=\frac{108^{\frac{1}{x}}}{x}\text{, }&x\neq 0\end{matrix}\right.$$