Solve 1/2000000=10^-x

$$\frac { 1 } { 2000000 } = 10 ^ { - x }$$

Solve for x

$$x=\log(2000000)\approx 6.301029996$$

Steps Using Definition of Logarithm

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

$$10^{-x}=\frac{1}{2000000}$$

Take the logarithm of both sides of the equation.

$$\log(10^{-x})=\log(\frac{1}{2000000})$$

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

$$-x\log(10)=\log(\frac{1}{2000000})$$

Divide both sides by -1.

$$x=-\frac{\log(2000000)}{-1}$$

Solve for x (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(10)}+\log_{10}\left(2000000\right)$$

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