Solve 360=300e^0.04x

$$360 = 300 e ^ { 0.04 x }$$

Solve for x

$$x=\ln(95.3962166440690129601298432)\approx 4.55803892$$

Steps Using Definition of Logarithm

Divide both sides by 300.

$$\frac{360}{300}=e^{0.04x}$$

Reduce the fraction \frac{360}{300} to lowest terms by extracting and canceling out 60.

$$\frac{6}{5}=e^{0.04x}$$

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

$$e^{0.04x}=\frac{6}{5}$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.04x})=\log(\frac{6}{5})$$

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

$$0.04x\log(e)=\log(\frac{6}{5})$$

Divide both sides by \log(e).

$$0.04x=\frac{\log(\frac{6}{5})}{\log(e)}$$

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

$$0.04x=\log_{e}\left(\frac{6}{5}\right)$$

Multiply both sides by 25.

$$x=\frac{\ln(\frac{6}{5})}{0.04}$$

Solve for x (complex solution)

$$x=\ln(95.3962166440690129601298432)+i\times 50\pi n_{1}$$

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