Solve 2=3e^1,2x

$$2 = 3 e ^ { 1,2 x }$$

Solve for x

$$x=\frac{5\ln(2)-5\ln(3)}{6}\approx -0.33788759$$

Steps Using Definition of Logarithm

Divide both sides by 3.

$$\frac{2}{3}=e^{1,2x}$$

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

$$e^{1,2x}=\frac{2}{3}$$

Take the logarithm of both sides of the equation.

$$\log(e^{1,2x})=\log(\frac{2}{3})$$

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

$$1,2x\log(e)=\log(\frac{2}{3})$$

Divide both sides by \log(e).

$$1,2x=\frac{\log(\frac{2}{3})}{\log(e)}$$

By the change-of-base formula log(a)/log(b)=log(b,a).

$$1,2x=\log_{e}\left(\frac{2}{3}\right)$$

Divide both sides of the equation by 1,2, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{\ln(\frac{2}{3})}{1,2}$$