Solve 4div10=2^x

$$4 \div 10 = { 2 }^{ x }$$

Solve for x

$$x=-\log_{2}\left(5\right)+1\approx -1.321928095$$

Steps Using Definition of Logarithm

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}=2^{x}$$

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

$$2^{x}=\frac{2}{5}$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(\frac{2}{5})$$

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

$$x\log(2)=\log(\frac{2}{5})$$

Divide both sides by \log(2).

$$x=\frac{\log(\frac{2}{5})}{\log(2)}$$

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

$$x=\log_{2}\left(\frac{2}{5}\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(\frac{2}{5}\right)$$

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