Question

Which four statements are true?

Answer 1

y = e^x and y = ln(x) are inverses

ln(e) = 1

ln(e^x) and e^ln(x) both equal x

ln(x) = log_e(x)

Step-by-step explanation:

To find the inverse of y = e^x, switch x and y, then isolate y.

y = e^x → x = e^y

ln(x) = ln(e^y)

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

ln (natural log) is defined as a logarithm of base e, so ln(x) = log_e(x)

ln(e) = log_e(e) ⇒ e^x = e ⇒ x = 1

ln and e are inverses, so they cancel each other out. Therefore, ln(e^x) and e^ln(x) both equal x