Solve 7^5x-4*2^4x-3=7^2x-3xa^x-2

$$7 ^ { 5 x - 4 } \times 2 ^ { 4 x - 3 } = 7 ^ { 2 x - 3 } x a ^ { x - 2 }$$

Solve for a (complex solution)

$$a=56^{\frac{-Re(x)+iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-4Re(x)+4}}\times 3136^{\frac{1}{\left(Re(x)-2\right)^{2}+\left(Im(x)\right)^{2}}}\times \left(\frac{|5488^{x}|}{|x|}\right)^{\frac{Re(x)-iIm(x)-2}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-4Re(x)+4}}e^{\frac{Im(x)arg(\frac{5488^{x}}{x})+iRe(x)arg(\frac{5488^{x}}{x})-2iarg(\frac{5488^{x}}{x})}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-4Re(x)+4}-\frac{2\pi n_{1}iRe(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-4Re(x)+4}-\frac{2\pi n_{1}Im(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-4Re(x)+4}+\frac{4\pi n_{1}i}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-4Re(x)+4}}$$

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

$$x\neq 0$$

Solve for a

$$\left\{\begin{matrix}a=\left(\frac{5488^{x}}{56x}\right)^{\frac{1}{x-2}}\text{, }&\left(Numerator(x-2)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x<0\right)\text{ or }\left(\left(\frac{5488^{x}}{56x}\right)^{\frac{1}{x-2}}>0\text{ and }x\neq 2\text{ and }x>0\right)\text{ or }\left(\left(\frac{5488^{x}}{56x}\right)^{\frac{1}{x-2}}<0\text{ and }x\neq 2\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x>0\right)\\a=-\left(\frac{5488^{x}}{56x}\right)^{\frac{1}{x-2}}\text{, }&\left(Numerator(x-2)\text{bmod}2=1\text{ and }x<0\text{ and }Numerator(x-2)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\right)\text{ or }\left(x>0\text{ and }x\neq 2\text{ and }\left(\frac{5488^{x}}{56x}\right)^{\frac{1}{x-2}}<0\text{ and }Numerator(x-2)\text{bmod}2=0\right)\text{ or }\left(x>0\text{ and }x\neq 2\text{ and }\left(\frac{5488^{x}}{56x}\right)^{\frac{1}{x-2}}>0\text{ and }Numerator(x-2)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\right)\end{matrix}\right.$$