Solve 800/272={(e)^0.00267x}

$$\frac{ 800 }{ 272 } = {(e)^{ 0.00267x }}$$

Solve for x

$$x=\frac{100000\ln(50)-100000\ln(17)}{267}\approx 404.048562312$$

Steps Using Definition of Logarithm

Reduce the fraction \frac{800}{272} to lowest terms by extracting and canceling out 16.

$$\frac{50}{17}=e^{0.00267x}$$

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

$$e^{0.00267x}=\frac{50}{17}$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.00267x})=\log(\frac{50}{17})$$

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

$$0.00267x\log(e)=\log(\frac{50}{17})$$

Divide both sides by \log(e).

$$0.00267x=\frac{\log(\frac{50}{17})}{\log(e)}$$

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

$$0.00267x=\log_{e}\left(\frac{50}{17}\right)$$

Divide both sides of the equation by 0.00267, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{\ln(\frac{50}{17})}{0.00267}$$

Solve for x (complex solution)

$$x=\frac{i\times 200000\pi n_{1}}{267}+\frac{100000\ln(50)}{267}-\frac{100000\ln(17)}{267}$$

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