Solve 1/2=e^-6.08x

$$\frac { 1 } { 2 } = e ^ { - 6.08 x }$$

Solve for x

$$x=\frac{25\ln(2)}{152}\approx 0.11400447$$

Steps Using Definition of Logarithm

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

$$e^{-6.08x}=\frac{1}{2}$$

Take the logarithm of both sides of the equation.

$$\log(e^{-6.08x})=\log(\frac{1}{2})$$

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

$$-6.08x\log(e)=\log(\frac{1}{2})$$

Divide both sides by \log(e).

$$-6.08x=\frac{\log(\frac{1}{2})}{\log(e)}$$

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

$$-6.08x=\log_{e}\left(\frac{1}{2}\right)$$

Divide both sides of the equation by -6.08, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=-\frac{\ln(2)}{-6.08}$$

Solve for x (complex solution)

$$x=-\frac{i\times 25\pi n_{1}}{76}+\frac{25\ln(2)}{152}$$

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