SOLUTION: log9^-1 + xlog(3^(5x-7))^(1/3) = 0 Find the exact value of x. Thanks!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: log9^-1 + xlog(3^(5x-7))^(1/3) = 0 Find the exact value of x. Thanks!      Log On


   

Question 1026585: log9^-1 + xlog(3^(5x-7))^(1/3) = 0 Find the exact value of x. Thanks!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
log9^-1 + xlog(3^(5x-7))^(1/3) = 0 Find the exact value of x. Thanks!
----------------------
-log(9) + x*log(3^[(5x-7)/3] = 0
--------
- log(9) = - log[3^(5x^2-7x)/3]
---------------------------
3^[5x^2-7x)/3 = 3^2
------------------------------
(5x^2-7x)/3 = 2
--------------------------
5x^2 - 7x - 6 = 0
---------
5x^2 - 10x+3x -6 = 0
-------
5x(x-2)+3(x-2) = 0
-------
(x-2)(5x+3) = 0
x = 2 or x = -3/5
----
Check for extraneous answers.
Cheers,
Stan H.
--------------