SOLUTION: Change to exponential form log 10^x + log 10 (x + 15) = 2 {{{log (10, x) + log (10, (x+15)) = 2}}}

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Question 4506: Change to exponential form
log 10^x + log 10 (x + 15) = 2
log+%2810%2C+x%29+%2B+log+%2810%2C+%28x%2B15%29%29+=+2
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
log+%2810%2C+x%29+%2B+log+%2810%2C+%28x%2B15%29%29+=+2

By the first law of logarithms, log M + log N = log MN
log+%2810%2C+x%28x%2B15%29%29+=+2

Convert from logarithmic notation to exponential form by writing this as
10%5E2+=+x%28x%2B15%29
100+=+x%5E2+%2B+15x

Set equal to zero:
0+=+x%5E2+%2B+15x+-+100

Factor the trinomial:
0+=+%28x+%2B+20%29%28x+-+5%29

Therefore x = -20 or x = 5.
However, if x = -20, then the original equation results in log (-20) + log (-5) which is not a real number, so this answer must be rejected.

Final answer is x = 5 the only possible solution.

R^2 at SCC