e^(3x-2)=150

Question

I need to solve e^(3x-2)=150.

Answer 1

The exponential equation is e^{3x - 2} = 150.

Take natural log of each side.

ln e^{3x - 2} = ln 150

Apply inverse property of natural logarithm: ln e^x = x.

3x - 2 = ln 150

3x = ln 150 + 2

x = 1/3 (ln 150 + 2)

x = 0.3333 (5.0106 + 2)

x = 0.3333 (7.0106)

x = 2.3368.

Solution of the equation is x = 1/3 (ln 150 + 2) or x = 2.3369.