Solve a*b^x=631

$$a \cdot b ^ { x } = 631$$

Solve for a (complex solution)

$$a=\frac{631}{b^{x}}$$

$$x=0\text{ or }b\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$b^{x}a=631$$

Divide both sides by b^{x}.

$$\frac{b^{x}a}{b^{x}}=\frac{631}{b^{x}}$$

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

$$a=\frac{631}{b^{x}}$$

Solve for a

$$a=\frac{631}{b^{x}}$$

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

Steps for Solving Linear Equation

The equation is in standard form.

$$b^{x}a=631$$

Divide both sides by b^{x}.

$$\frac{b^{x}a}{b^{x}}=\frac{631}{b^{x}}$$

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

$$a=\frac{631}{b^{x}}$$

Solve for b (complex solution)

$$b=e^{-\frac{2\pi n_{1}iRe(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}-\frac{2\pi n_{1}Im(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}+\frac{arg(\frac{1}{a})Im(x)+iarg(\frac{1}{a})Re(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\times \left(\frac{631}{|a|}\right)^{\frac{Re(x)-iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}$$

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

$$a\neq 0$$

Solve for b

$$\left\{\begin{matrix}b=\left(\frac{631}{a}\right)^{\frac{1}{x}}\text{, }&\left(Numerator(x)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }\left(\frac{631}{a}\right)^{\frac{1}{x}}\neq 0\text{ and }a<0\right)\text{ or }\left(\left(\frac{631}{a}\right)^{\frac{1}{x}}>0\text{ and }x\neq 0\text{ and }a>0\right)\text{ or }\left(\left(\frac{631}{a}\right)^{\frac{1}{x}}<0\text{ and }x\neq 0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }a>0\right)\\b=-\left(\frac{631}{a}\right)^{\frac{1}{x}}\text{, }&\left(a<0\text{ and }Numerator(x)\text{bmod}2=1\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }\left(\frac{631}{a}\right)^{\frac{1}{x}}\neq 0\right)\text{ or }\left(a>0\text{ and }x\neq 0\text{ and }\left(\frac{631}{a}\right)^{\frac{1}{x}}<0\text{ and }Numerator(x)\text{bmod}2=0\right)\text{ or }\left(a>0\text{ and }x\neq 0\text{ and }\left(\frac{631}{a}\right)^{\frac{1}{x}}>0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\right)\\b\neq 0\text{, }&a=631\text{ and }x=0\end{matrix}\right.$$