SOLUTION: Hi i need help with this problem please log4(x-4)=3-log(x+8)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi i need help with this problem please log4(x-4)=3-log(x+8)      Log On


   

Question 747840: Hi i need help with this problem please
log4(x-4)=3-log(x+8)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2Cx-4%29=3-log%28x%2B8%29....I guess you have log%284%2C%28x%2B8%29%29
if so, then you have
log%284%2C%28x-4%29%29=3-log%284%2C%28x%2B8%29%29
log%284%2C%28x-4%29%29%2Blog%284%2C%28x%2B8%29%29=3
log%28x-4%29%2Flog%284%29%2Blog%28x%2B8%29%2Flog%284%29=3
%28log%28x-4%29%2Blog%28x%2B8%29%29%2Flog%284%29=3
log%28x-4%29%2Blog%28x%2B8%29=3log%284%29
log%28x-4%29%2Blog%28x%2B8%29=log%284%5E3%29
log%28%28x-4%29%28x%2B8%29%29=log%2864%29
%28x-4%29%28x%2B8%29=64
x%5E2%2B8x-4x-32=64
x%5E2%2B4x-32-64=0
x%5E2%2B4x-96=0....write 4x as 12x-8x
x%5E2%2B12x-8x-96=0..group
%28x%5E2%2B12x%29-%288x%2B96%29=0
x%28x%2B12%29-8%28x%2B12%29=0
%28x-8%29%28x%2B12%29=0
solutions:
if x-8=0 => x=8
if x%2B12=0 => x=-12
your solution is: highlight%28x=8%29
recall:
The logarithmic function
y+=+log%28b%2Cx%29
is the inverse function of the exponential function
x+=+b%5Ey
Since the base b is positive (b%3E0), the base b raised to the power of y must be positive (b%5Ey%3E0) for any real y. So the number x must be positive (x%3E0).
The real base b logarithm of a negative number is undefined.
log%28b%2Cx%29 is undefined for x+%3C=+0
For example, the base log%2810%2C+-5%29 is undefined.
so, if x=-12, logarithm is undefined