Solve 66440000=0.2851*{(e)^0.2825x}

$$66440000=0.2851 \times {(e)^{ 0.2825x }}$$

Solve for x

$$x=\frac{400\ln(664400000000)-400\ln(2851)}{113}\approx 68.200796905$$

Steps Using Definition of Logarithm

Divide both sides by 0.2851.

$$\frac{66440000}{0.2851}=e^{0.2825x}$$

Expand \frac{66440000}{0.2851} by multiplying both numerator and the denominator by 10000.

$$\frac{664400000000}{2851}=e^{0.2825x}$$

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

$$e^{0.2825x}=\frac{664400000000}{2851}$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.2825x})=\log(\frac{664400000000}{2851})$$

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

$$0.2825x\log(e)=\log(\frac{664400000000}{2851})$$

Divide both sides by \log(e).

$$0.2825x=\frac{\log(\frac{664400000000}{2851})}{\log(e)}$$

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

$$0.2825x=\log_{e}\left(\frac{664400000000}{2851}\right)$$

Divide both sides of the equation by 0.2825, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{\ln(\frac{664400000000}{2851})}{0.2825}$$

Solve for x (complex solution)

$$x=\frac{i\times 800\pi n_{1}}{113}+\frac{400\ln(664400000000)}{113}-\frac{400\ln(2851)}{113}$$

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