What is x if Ln9+ln4x^2=2?

1 Answer
May 4, 2018

We wish to find #x# if #ln9 + ln(4x^2) = 2#. We will need to use some log rules here. Specifically, recall that:

#lnx + lny = ln(xy)#
#e^(ln(x)) = x#

Using the above two rules, we can quickly come to an answer.

#ln 9 + ln(4x^2) = 2# (Use Rule 1 to combine.)
#ln(9*4x^2) = 2#
#ln(36x^2) = 2# (Use Rule 2 and exponentiate both sides.)
#36x^2 = e^2#
#x^2 = e^2/(36) = (e/6)^2#
#x = pm e/6#