SOLUTION: Good evening to all I have some difficult to understand the difference between following two logarithmic equations a) log2(x^2 - 4x) =5 with solutions x=-4 V x=8 b) log2(x)

Question 1012139: Good evening to all
I have some difficult to understand the difference between following
two logarithmic equations
a) log2(x^2 - 4x) =5 with solutions x=-4 V x=8
b) log2(x) + log2(x-4) = 5 with only one solution x = 8
As I know from log. properties the sum of 2 logarithms is the product of the
arguments, so equation b) gives the product of arguments x^2 - 4x
Where do I wrong?
My thanks in advance

Found 2 solutions by Boreal, josgarithmetic:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
log2(x) + log2(x-4) = 5
log2 (x^2-4x)=5
raise everything to the 2 power
x^2-4x=32
x^2-4x-32=0
(x-8)(x+4)=0
x=8, -4, but can't take a log of a negative number so there is only one solution.
If the log is of (x^2-4x), then x=-4 works.
As soon as you multiply the two together, you have slightly changed the form of the equation. With quadratics and logs, it is necessary to put the root found back into the original equation to see if it works. Often, one does not.
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
(a)

----correct but unnecessary

-----quadratic equation

(b)
----this as the original equation is in a different form given. We just do not have log of a negative number, . Base two to no power will give negative number.
RELATED QUESTIONS
Good evening Friends, I have some difficulties solving the following logarithmic... (answered by ikleyn)
.Good evening, can I please have some help on this one, i got x=8 please please show the... (answered by stanbon)
Good evening, I have some difficulties with this logarithmic equation:... (answered by Boreal,Theo,MathTherapy)
Hi Please help me tell the difference between a logarithmic function and a logarithmic... (answered by stanbon)
I am having a bit of difficulty understanding some basic logarithmic equations, whilst i... (answered by jsmallt9)
good evening, I am not sure if this is where I need to ask the question on solving... (answered by ankor@dixie-net.com)
We are currently working on logarithmic functions, and we are given two equations that... (answered by josgarithmetic,Theo)
I am trying to do logarithmic equations and is having a difficult time finding a... (answered by lwsshak3)
I sure hope some one is feeling good this evening as im not good with this stuff and i... (answered by jim_thompson5910)