SOLUTION: e^(ln(4 x))=16 what does x=? thanks!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: e^(ln(4 x))=16 what does x=? thanks!      Log On


   

Question 1000151: e^(ln(4 x))=16
what does x=?
thanks!
Found 2 solutions by fractalier, josmiceli:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
In the expression
e%5E%28ln%284+x%29%29=16
exponentiating and taking the log are inverses, so that
4x = 16
and
x = 4

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have to know how to read this.
The left side says:
e^[ some exponent ]
The exponent that +e+ is raised to reads as:
" I am an exponent ( natural log ) that gives you
+4x+ when the base is +e+ "
-----------------------------
You do have this exponent with the base +e+
on the left side, so the expression is +4x+
Then,
+4x+=+16+
+x+=+4+
--------------------------------------
A simpler example of this would be:
+10%5E%28+log%28+100+%29%29+=+x+
What is +x+ ?
The left side says:
" I am +10+ raised to an exponent "
The exponent says:
" I am an exponent and if my base is +10+,
then I give you +100+ "
The base is +10+, so the left side equals +100+
+x+=+100+