Solve 2700=1800e^19h

$$2700 = 1800 e ^ { 19 h }$$

Solve for h

$$h=\frac{\ln(\frac{3}{2})}{19}\approx 0.021340269$$

Steps Using Definition of Logarithm

Divide both sides by 1800.

$$\frac{2700}{1800}=e^{19h}$$

Reduce the fraction \frac{2700}{1800} to lowest terms by extracting and canceling out 900.

$$\frac{3}{2}=e^{19h}$$

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

$$e^{19h}=\frac{3}{2}$$

Take the logarithm of both sides of the equation.

$$\log(e^{19h})=\log(\frac{3}{2})$$

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

$$19h\log(e)=\log(\frac{3}{2})$$

Divide both sides by \log(e).

$$19h=\frac{\log(\frac{3}{2})}{\log(e)}$$

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

$$19h=\log_{e}\left(\frac{3}{2}\right)$$

Divide both sides by 19.

$$h=\frac{\ln(\frac{3}{2})}{19}$$

Solve for h (complex solution)

$$h=\frac{2\pi n_{1}i}{19}+\frac{\ln(\frac{3}{2})}{19}$$

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