How do you solve #ln(x)=2#?

Question

9583 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-30T22:52:39

#=>x = e^2#

#=>ln(x) = 2#

Natural log has a base of #e#. More explicitly we can write:

#=>ln_e(x) = 2#

Logarithms have the following form:

#=>log_a(x) = b#

They also have the property:

#=>a^(log_a(x)) = x#

So we can raise both sides of our equation by #e# to extract the #x#:

#=>e^(ln(x)) = e^2#

#=>x = e^2#