Solve 1300=1000e^1x

$$1300 = 1000 e ^ { 1 x }$$

Solve for x

$$x=\ln(\frac{13}{10})\approx 0.262364264$$

Steps Using Definition of Logarithm

Divide both sides by 1000.

$$\frac{1300}{1000}=e^{1x}$$

Reduce the fraction \frac{1300}{1000} to lowest terms by extracting and canceling out 100.

$$\frac{13}{10}=e^{1x}$$

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

$$e^{1x}=\frac{13}{10}$$

Reorder the terms.

$$e^{x}=\frac{13}{10}$$

Take the logarithm of both sides of the equation.

$$\log(e^{x})=\log(\frac{13}{10})$$

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

$$x\log(e)=\log(\frac{13}{10})$$

Divide both sides by \log(e).

$$x=\frac{\log(\frac{13}{10})}{\log(e)}$$

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

$$x=\log_{e}\left(\frac{13}{10}\right)$$

Solve for x (complex solution)

$$x=\ln(\frac{13}{10})+2\pi n_{1}i$$

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