Solve 10^2x/10^4=100^2

$$\frac { 10 ^ { 2 x } } { 10 ^ { 4 } } = 100 ^ { 2 }$$

Solve for x

$$x=4$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$\frac{1}{10000}\times 10^{2x}=10000$$

Multiply both sides by 10000.

$$10^{2x}=100000000$$

Take the logarithm of both sides of the equation.

$$\log(10^{2x})=\log(100000000)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$2x\log(10)=\log(100000000)$$

Divide both sides by 2.

$$x=\frac{8}{2}$$

Solve for x (complex solution)

$$x=4+\pi n_{1}i\log(e)$$

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