Solve 400000=200000*104^x

$$400000=200000 \times { 104 }^{ x }$$

Solve for x

$$x=\log_{104}\left(2\right)\approx 0.149243937$$

Steps Using Definition of Logarithm

Divide both sides by 200000.

$$\frac{400000}{200000}=104^{x}$$

Divide 400000 by 200000 to get 2.

$$2=104^{x}$$

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

$$104^{x}=2$$

Take the logarithm of both sides of the equation.

$$\log(104^{x})=\log(2)$$

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

$$x\log(104)=\log(2)$$

Divide both sides by \log(104).

$$x=\frac{\log(2)}{\log(104)}$$

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

$$x=\log_{104}\left(2\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(104)}+\log_{104}\left(2\right)$$

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