SOLUTION: Solve the logarithmic equation and express irrational solutions in lowest radical form. log(x) + log(x+15) = 2 I just can't seem to grasp how to solve this.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the logarithmic equation and express irrational solutions in lowest radical form. log(x) + log(x+15) = 2 I just can't seem to grasp how to solve this.      Log On


   

Question 83401: Solve the logarithmic equation and express irrational solutions in lowest radical form.
log(x) + log(x+15) = 2
I just can't seem to grasp how to solve this.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
log(x) + log(x+15) = 2
log%2810%2C%28x%29%29+%2B+log%2810%2C%28x%2B15%29%29+=+2

Use the first law of logarithms to form a single logarithm:
log%2810%2Cx%28x%2B15%29%29=2

Using the basic definition, convert to exponential form:
10%5E2+=+x%28x%2B15%29
100+=+x%5E2+%2B+15x+
0=x%5E2+%2B+15x+-100+

Solve the quadratic formula by factoring if possible, otherwise the quadratic formula or completing the square:
0=%28x-20%29%28x%2B5%29+ (Isn't it nice when these kinds of problems factor? )
x=20 or x=-5

You must check these answers to make sure that none of the values of x make a log of a negative (logs of negatives are not allowed in the real numbers!!). Therefore, the answer x=-5 must be rejected.

The final answer is x=+20.

R^2 at SCC