SOLUTION: Solve, and express you answer in exact form: log(x) + ln(x) = 1

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Question 64622: Solve, and express you answer in exact form: log(x) + ln(x) = 1
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The first step is to get everything into the same base logarithm, by using the formula log+%2810%2Cx%29+=+%28ln+x%29%2F%28ln+10%29+.

log(x) + ln(x) = 1
%28ln+x%29%2F%28ln+10%29+%2Bln+x+=+1+.

You might want to clear the fraction by multiplying both sides times ln 10:
ln+x+%2B+%28ln+10%29%2A%28ln+x%29+=+ln+10

Next, factor the ln x, which is a common factor on the left side:
%28ln+x%29+%2A%281+%2B+ln+10%29+=+ln+10

Divide both sides by (1 + ln 10)
ln+x+=+%28ln+10%29%2F%281%2B+ln+10%29+

Raise both sides as a power of e:
x+=+e%5E%28%28ln+10%29%2F%281%2B+ln+10%29%29+

R^2 at SCC

P.S. Nice problem!!!