Solve frac{5^{x-2}*2^x+2}{2^x-2*5^x-6}=100^xd

$$\frac { 5 ^ { x - 2 } \cdot 2 ^ { x + 2 } } { 2 ^ { x - 2 } \cdot 5 ^ { x - 6 } } = 100 ^ { x } d$$

Solve for d

$$d=\frac{10000}{10^{2x}}$$

Steps for Solving Linear Equation

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

$$100^{x}d=\frac{5^{x-2}\times 2^{x+2}}{2^{x-2}\times 5^{x-6}}$$

The equation is in standard form.

$$100^{x}d=10000$$

Divide both sides by 100^{x}.

$$\frac{100^{x}d}{100^{x}}=\frac{10000}{100^{x}}$$

Dividing by 100^{x} undoes the multiplication by 100^{x}.

$$d=\frac{10000}{100^{x}}$$

Divide 10000 by 100^{x}.

$$d=10^{4-2x}$$

Solve for x (complex solution)

$$x=-\frac{\log(d)}{2}+2+\pi n_{1}i\log(e)$$

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

$$d\neq 0$$

Solve for x

$$x=-\frac{\log(d)}{2}+2$$

$$d>0$$