Solve y=a^x-(b+1)

$$y = a ^ { x } - ( b + 1 )$$

Solve for b (complex solution)

$$b=-y+a^{x}-1$$

Steps for Solving Linear Equation

To find the opposite of b+1, find the opposite of each term.

$$y=a^{x}-b-1$$

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

$$a^{x}-b-1=y$$

Subtract a^{x} from both sides.

$$-b-1=y-a^{x}$$

Add 1 to both sides.

$$-b=y-a^{x}+1$$

Divide both sides by -1.

$$\frac{-b}{-1}=\frac{y-a^{x}+1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=\frac{y-a^{x}+1}{-1}$$

Divide y-a^{x}+1 by -1.

$$b=-y+a^{x}-1$$

Solve for b

$$b=-y+a^{x}-1$$

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

Steps for Solving Linear Equation

To find the opposite of b+1, find the opposite of each term.

$$y=a^{x}-b-1$$

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

$$a^{x}-b-1=y$$

Subtract a^{x} from both sides.

$$-b-1=y-a^{x}$$

Add 1 to both sides.

$$-b=y-a^{x}+1$$

Divide both sides by -1.

$$\frac{-b}{-1}=\frac{y-a^{x}+1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=\frac{y-a^{x}+1}{-1}$$

Divide y-a^{x}+1 by -1.

$$b=-y+a^{x}-1$$

Solve for a (complex solution)

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

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