Solve (-2)^4x(-2)^7=(-2)^p+1quad

$$( - 2 ) ^ { 4 } x ( - 2 ) ^ { 7 } = ( - 2 ) ^ { p + 1 } \quad$$

Solve for x (complex solution)

$$x=\frac{\left(-2\right)^{p}}{1024}$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\left(-2\right)^{11}x=\left(-2\right)^{p+1}$$

Calculate -2 to the power of 11 and get -2048.

$$-2048x=\left(-2\right)^{p+1}$$

Divide both sides by -2048.

$$\frac{-2048x}{-2048}=\frac{\left(-2\right)^{p+1}}{-2048}$$

Dividing by -2048 undoes the multiplication by -2048.

$$x=\frac{\left(-2\right)^{p+1}}{-2048}$$

Divide \left(-2\right)^{1+p} by -2048.

$$x=\frac{\left(-2\right)^{p}}{1024}$$

Solve for x

$$x=\frac{\left(-2\right)^{p}}{1024}$$

$$Denominator(p)\text{bmod}2=1$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\left(-2\right)^{11}x=\left(-2\right)^{p+1}$$

Calculate -2 to the power of 11 and get -2048.

$$-2048x=\left(-2\right)^{p+1}$$

Divide both sides by -2048.

$$\frac{-2048x}{-2048}=\frac{\left(-2\right)^{p+1}}{-2048}$$

Dividing by -2048 undoes the multiplication by -2048.

$$x=\frac{\left(-2\right)^{p+1}}{-2048}$$

Divide \left(-2\right)^{1+p} by -2048.

$$x=\frac{\left(-2\right)^{p}}{1024}$$

Solve for p (complex solution)

$$p=\frac{\ln(-2048x)-\pi i-\ln(2)}{\ln(2)+\pi i}+\frac{2\pi n_{1}i}{\ln(2)+\pi i}$$

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

$$x\neq 0$$

Solve for p

$$p=\log_{2}\left(-2048x\right)-1$$

$$x<0\text{ and }Numerator(\log_{2}\left(-2048x\right))\text{bmod}2=0\text{ and }Denominator(\log_{2}\left(-2048x\right))\text{bmod}2=1$$