Question 393174: How do you solve 2log[base 6](x)-2log[base 6] (x-4)= 1
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve 2log[base 6](x)-2log[base 6] (x-4)= 1
-------------
Divide thru by 2 to get:
log6(x)-log6(x-4) = 1/2
---
log6[x(x-4)] = 1/2
----
x(x-4) = 6^(1/2)
----
x^2-4x-6^(1/2) = 0
-----
Use the Quadratic formula to find a positive solution
because x must be positive in the original problem statement:
x = [4 + sqrt(16-4*6^(1/2))]/2
---
x = [4 + sqrt(6.202)]/2
---
x = 3.245..
-----------
That is not an acceptable answer because 3.234-4 is negative
and you cannot take a log of a negative number.
---------
Conclusion: No solution
===========================
Cheers,
Stan H.
|
|
|
