Solve 10=2.44*{(e)^-0.0866*x}

$$10=2.44 \times {(e)^{ -0.0866 \times x }}$$

Solve for x

$$x=\frac{5000\ln(61)-5000\ln(250)}{433}\approx -16.288534107$$

Steps Using Definition of Logarithm

Divide both sides by 2.44.

$$\frac{10}{2.44}=e^{-0.0866x}$$

Expand \frac{10}{2.44} by multiplying both numerator and the denominator by 100.

$$\frac{1000}{244}=e^{-0.0866x}$$

Reduce the fraction \frac{1000}{244} to lowest terms by extracting and canceling out 4.

$$\frac{250}{61}=e^{-0.0866x}$$

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

$$e^{-0.0866x}=\frac{250}{61}$$

Take the logarithm of both sides of the equation.

$$\log(e^{-0.0866x})=\log(\frac{250}{61})$$

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

$$-0.0866x\log(e)=\log(\frac{250}{61})$$

Divide both sides by \log(e).

$$-0.0866x=\frac{\log(\frac{250}{61})}{\log(e)}$$

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

$$-0.0866x=\log_{e}\left(\frac{250}{61}\right)$$

Divide both sides of the equation by -0.0866, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{\ln(\frac{250}{61})}{-0.0866}$$

Solve for x (complex solution)

$$x=-\frac{i\times 10000\pi n_{1}}{433}+\frac{5000\ln(61)}{433}-\frac{5000\ln(250)}{433}$$

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