If ln(x)=y how can we solve for x?

Answer 1

Use the definition of the natural log:
ln (a) = c means a = e^c.

So here, x = e^y by definition.

Answer 2

Put y = ln(x) (Power e both sides)

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

So, e^y = x => function f

Discontinuity at asymptote x = 0 on the plane (x,y) (graphic)

Dom f = ] 0, infinity => possible values for x
Ima f = ] 0, infinity => possible values for y

Answer : x => ]0, infinity ( x take only positive values without 0)

Answer 3

take the exponential of y, this will cancel the ln (x)

so ln(x) = y

take exponential

x = exp to the power of y

Answer 4

you raise both sides by e

e^ln(x)=e^y

e^ln cancels out leaving you with x=e^y
That's as far as you can go. Good luck!

Answer 5

If you have ln(x) = y, then:

e^[ln(x)] = e^y, or:

x = e^y

where e, the base of the natural logarithm, is equal to 2.71828182845904523536