Question

Solve for x: ln x = 0.863. Report your answer to 3 significant figures.

Answer 1

Answer:

x = 2.37

Explanation:

ln x = 0.863

apply e to both sides of the equation:

e^(ln x) = e^0.863

e^(ln x) = x  = e^0.863

{Demonstration of e^(ln x) = x:

y = e^(ln x)

apply ln to both sides of the equation:

ln y = ln (e^(ln x))

apply logarithmic property (ln xⁿ = n ln x)

ln y = ln x * ln e          (ln e = 1)

ln y = ln x

Then:

y = x

Because y = e^(ln x) and x = y, then:

x = e^(ln x)

End of the demonstration }

Returning to our equation:

e^(ln x) = e^0.863

Then,

x = e^0.863 = 2.37