Solve 1920=1600e^365x

$$1920 = 1600 e ^ { 365 x }$$

Solve for x

$$x=\frac{\ln(\frac{6}{5})}{365}\approx 0.000499511$$

Steps Using Definition of Logarithm

Divide both sides by 1600.

$$\frac{1920}{1600}=e^{365x}$$

Reduce the fraction \frac{1920}{1600} to lowest terms by extracting and canceling out 320.

$$\frac{6}{5}=e^{365x}$$

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

$$e^{365x}=\frac{6}{5}$$

Take the logarithm of both sides of the equation.

$$\log(e^{365x})=\log(\frac{6}{5})$$

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

$$365x\log(e)=\log(\frac{6}{5})$$

Divide both sides by \log(e).

$$365x=\frac{\log(\frac{6}{5})}{\log(e)}$$

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

$$365x=\log_{e}\left(\frac{6}{5}\right)$$

Divide both sides by 365.

$$x=\frac{\ln(\frac{6}{5})}{365}$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{365}+\frac{\ln(\frac{6}{5})}{365}$$

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