Solve 0.0000003=3*10^x

$$0.0000003 = 3 \times 10 ^ { x }$$

Solve for x

$$x=-7$$

Steps Using Definition of Logarithm

Divide both sides by 3.

$$\frac{0.0000003}{3}=10^{x}$$

Expand \frac{0.0000003}{3} by multiplying both numerator and the denominator by 10000000.

$$\frac{3}{30000000}=10^{x}$$

Reduce the fraction \frac{3}{30000000} to lowest terms by extracting and canceling out 3.

$$\frac{1}{10000000}=10^{x}$$

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

$$10^{x}=\frac{1}{10000000}$$

Take the logarithm of both sides of the equation.

$$\log(10^{x})=\log(\frac{1}{10000000})$$

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

$$x\log(10)=\log(\frac{1}{10000000})$$

Solve for x (complex solution)

$$x=-7+i\times 2\pi n_{1}\log(e)$$

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