solve e^x = y for x — step-by-step solution

Let's solve in

ℝ

e^{x} = y

The logarithm being defined only for positive numbers, let's apply the ln function on both sides, provided that

y > 0

\ln (e^{x}) = \ln (y)

ⓘ For real

x

\ln (\exp (x)) = x

; wherever

\ln (x)

is defined,

\exp (\ln (x)) = x

\ln (e^{x})

x

Solution found:

x = \ln (y)

Let's solve for y:

y > 0

Solution found:

y > 0

▶Solution:

{x = \ln (y), y > 0}