Solve 0.3=0.067*2^x

$$0.3 = 0.067 \times { 2 }^{ x }$$

Solve for x

$$x=\log_{2}\left(\frac{300}{67}\right)\approx 2.1627295$$

Steps Using Definition of Logarithm

Divide both sides by 0.067.

$$\frac{0.3}{0.067}=2^{x}$$

Expand \frac{0.3}{0.067} by multiplying both numerator and the denominator by 1000.

$$\frac{300}{67}=2^{x}$$

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

$$2^{x}=\frac{300}{67}$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(\frac{300}{67})$$

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

$$x\log(2)=\log(\frac{300}{67})$$

Divide both sides by \log(2).

$$x=\frac{\log(\frac{300}{67})}{\log(2)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{2}\left(\frac{300}{67}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(2)}+\log_{2}\left(\frac{300}{67}\right)$$

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