SOLUTION: solve equation express irrational in exact form and also as a decimal rounded 3 places log (x-4)+log (x+4)=2

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Question 381548: solve equation express irrational in exact form and also as a decimal rounded 3 places
log (x-4)+log (x+4)=2
Found 2 solutions by Fombitz, rapaljer:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
log+%2810%2C%28x-4%29%29%2Blog+%2810%2C%28x%2B4%29%29=2
log+%2810%2C%28%28x-4%29%28x%2B4%29%29%29=2
%28x-4%29%28x%2B4%29=10%5E2
x%5E2-16=100
x%5E2=116
x=0+%2B-+sqrt%28116%29
x=0+%2B-+2%2Asqrt%2829%29
Since the log function requires a positive argument,
highlight%28x=2%2Asqrt%2829%29%29 or approximately,
x=10.7703

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C%28x-4%29%29%2Blog%2810%2C%28x%2B4%29%29=2
log%2810%2C%28%28x-4%29%28x%2B4%29%29%29=2
log%2810%2C%28x%5E2-16%29%29=2
10%5E2=x%5E2-16
0=x%5E2-16-100
x%5E2-116=0
x%5E2=116
x=sqrt%28116%29 or x=-sqrt%28116%29

x=2%2Asqrt%2829%29 Reject the negative answer, since it gives a log of a negative number, which is NOT allowed.

You will have to calculate the decimal approximation yourself! I'm on vacation for a few days, and I didn't bring my calculator!!

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In addition, I have FREE videos from my classes before I retired of me teaching LOGARITHMS. To see my videos, look for "Rapalje Videos in Living Color." Again, choose "College Algebra," and look for the appropriate topic.

If you like my explanations, all I ask is that you recommend them to friends and family!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus