SOLUTION: solve each equation for x. 4+10^3-x=106 ln(x^2+x)=1

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Question 189948: solve each equation for x.
4+10^3-x=106
ln(x^2+x)=1
Answer by cutepiscean5(19) About Me  (Show Source):
You can put this solution on YOUR website!
Lets take the first equation:
4+10^3-x=106
I shall consider the given equation written as:
+4+%2B+10%5E%283-x%29+=+106+
=> +10%5E%283-x%29+=+106+-+4
=> +10%5E%283-x%29+=+102+
Taking log on both sides of the equation we get:
=> +log+10%5E%283-x%29+=+log+%28102%29+
using the log properties that: +log%28a%5Em%29+=+mlog%28a%29+, we get:
=> +%283-x%29log%2810%29+=+log%28102%29+
using log(10) = 1 and log(102) = 2.0086, we get:
=> +3-x+=+2.0086+
=> +x+=+3+-+2.0086+
=> +x+=+0.9913+

solving the second equation we get:
ln(x^2+x)=1
using the log property that if, +ln%28a%29+=+x+ , then +a+=+e%5Ex+, we get:
+x%5E2+%2B+x+=+e%5E1+
=> +x%5E2+%2B+x+-+e+=+0+
Solving using the quadratic formula we get:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
here , a = 1, b = 1 and c = -e
thus,
x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-e%29+%29%29%2F%282%2A1%29+
or,
+x+=+%28-1+%2B+sqrt%28+1+%2B+4%2Ae%29%29%2F2+ , and
+x+=+%28-1+-+sqrt%28+1+%2B+4%2Ae%29%29%2F2+
you can further simplify this by plugging in the value of e as 2.718, and solving. It depends on how the answer is required.