Solve x_{1}f^xp_{4}=42^xp_{2}

$$x _ { 1 } f ^ { x } p _ { 4 } = 42 ^ { x } p _ { 2 }$$

Solve for p_2 (complex solution)

$$p_{2}=p_{4}x_{1}\times \left(\frac{f}{42}\right)^{x}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$42^{x}p_{2}=x_{1}f^{x}p_{4}$$

The equation is in standard form.

$$42^{x}p_{2}=p_{4}x_{1}f^{x}$$

Divide both sides by 42^{x}.

$$\frac{42^{x}p_{2}}{42^{x}}=\frac{p_{4}x_{1}f^{x}}{42^{x}}$$

Dividing by 42^{x} undoes the multiplication by 42^{x}.

$$p_{2}=\frac{p_{4}x_{1}f^{x}}{42^{x}}$$

Divide x_{1}f^{x}p_{4} by 42^{x}.

$$p_{2}=p_{4}x_{1}\times \left(\frac{f}{42}\right)^{x}$$

Solve for p_2

$$p_{2}=p_{4}x_{1}\times \left(\frac{f}{42}\right)^{x}$$

$$\left(f<0\text{ and }Denominator(x)\text{bmod}2=1\right)\text{ or }\left(f=0\text{ and }x>0\right)\text{ or }f>0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$42^{x}p_{2}=x_{1}f^{x}p_{4}$$

The equation is in standard form.

$$42^{x}p_{2}=p_{4}x_{1}f^{x}$$

Divide both sides by 42^{x}.

$$\frac{42^{x}p_{2}}{42^{x}}=\frac{p_{4}x_{1}f^{x}}{42^{x}}$$

Dividing by 42^{x} undoes the multiplication by 42^{x}.

$$p_{2}=\frac{p_{4}x_{1}f^{x}}{42^{x}}$$

Divide x_{1}f^{x}p_{4} by 42^{x}.

$$p_{2}=p_{4}x_{1}\times \left(\frac{f}{42}\right)^{x}$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=e^{\frac{Im(x)arg(\frac{p_{2}\times 42^{x}}{p_{4}x_{1}})+iRe(x)arg(\frac{p_{2}\times 42^{x}}{p_{4}x_{1}})}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}-\frac{2\pi n_{1}iRe(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}-\frac{2\pi n_{1}Im(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\times \left(\frac{|p_{2}||42^{x}|}{|p_{4}||x_{1}|}\right)^{\frac{Re(x)-iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\text{, }n_{1}\in \mathrm{Z}\text{, }&p_{4}x_{1}\neq 0\\f\in \mathrm{C}\text{, }&\left(p_{4}=0\text{ or }x_{1}=0\right)\text{ and }p_{2}=0\end{matrix}\right.$$