Question

How are ln x and e^x inverses of each other?

Answer 1

Heyy there! I am AncientEnigma29 and I will be answering your question step by step

Step 1:

$\sf \: f(x) = ln(x)$

Replace f(x) with y

$\sf \: y = ln(x)$

Step 2:

Swap x and y with each other

$\tt \: x = ln(y)$

Step 3:

Solve for y...

• To do this we need to write x=ln(y) in exponential form.
• Recognize that ln(y) is a logarithm with base e, where e has approximate value of 2.71828.

$\bf \: ln(y) = log e (y)$

Rule of log used: $\boxed{ \rm \:c = log_{a}b \: then \: {a}^{c} = b }$

By the rule we have, x=ln(y) is equal to y=e^x

Step 4:

Replace y with f^-1 (x)

$\mathcal{ {f}^{ - 1}(x) = {e}^{x} }$