SOLUTION: Solve the following logarithmic equation. log(base 2)x+16+log(base 2)x+10=4. Show all work.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the following logarithmic equation. log(base 2)x+16+log(base 2)x+10=4. Show all work.      Log On


   

Question 639940: Solve the following logarithmic equation. log(base 2)x+16+log(base 2)x+10=4. Show all work.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following logarithmic equation. log(base 2)x+16+log(base 2)x+10=4. Show all work.
rewrite equation:
log2(x+16)+log2(x+10)=4
place under single log
log2[(x+16)(x+10)]=4
convert to exponential form
2^4=[(x+16)(x+10)
x^2+26x+160=16
x^2+26x+144=0
(x+8)(x+18)=0
x=-18 (reject, (x+10)>0)
x=-8