Solve 300000*1.004^x=630000

$$300000 \times { 1.004 }^{ x } =630000$$

Solve for x

$$x=\log_{1.004}\left(2.1\right)\approx 185.855058036$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$300000\times 1.004^{x}=630000$$

Divide both sides by 300000.

$$1.004^{x}=\frac{21}{10}$$

Take the logarithm of both sides of the equation.

$$\log(1.004^{x})=\log(\frac{21}{10})$$

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

$$x\log(1.004)=\log(\frac{21}{10})$$

Divide both sides by \log(1.004).

$$x=\frac{\log(\frac{21}{10})}{\log(1.004)}$$

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

$$x=\log_{1.004}\left(\frac{21}{10}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.004)}+\log_{1.004}\left(2.1\right)$$

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