Question 1058666: Solve for x, to three significant digits: 2^4x + 2^2x = 132.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve for x, to three significant digits: 2^4x + 2^2x = 132.
----
2^(4x) + 2^(2x) = 132
-------
4^(2x) + 4^x - 132 = 0
----
(4^x)^2 + 4^x - 132 = 0
-----
Factor::
Let w = 4^x
w^2 + w - 132 = 0
(w-11)(w+12) = 0
-----
w = 11 or w = -12
------
Solve for "x":
4^x = 11
x = log(11)/log(4) = 1.730
-------------------
OR
4^x = -12
Comment:: No power of 4 can be negative.
---------------------
Only solution:: x = 1.730
-------------
Cheers,
Stan H.
--------------
|
|
|
