Solve 10000*391000000=2^x

$$10000 \times 391000000= { 2 }^{ x }$$

Solve for x

$$x=\log_{2}\left(3910000000000\right)\approx 41.830305746$$

Steps Using Definition of Logarithm

Multiply 10000 and 391000000 to get 3910000000000.

$$3910000000000=2^{x}$$

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

$$2^{x}=3910000000000$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(3910000000000)$$

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

$$x\log(2)=\log(3910000000000)$$

Divide both sides by \log(2).

$$x=\frac{\log(3910000000000)}{\log(2)}$$

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

$$x=\log_{2}\left(3910000000000\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(3910000000000\right)$$

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