SOLUTION: Please help. log base3(x-2)+log base3(x+4)=3 e^x+5=8

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help. log base3(x-2)+log base3(x+4)=3 e^x+5=8       Log On


   

Question 64477: Please help.
log base3(x-2)+log base3(x+4)=3
e^x+5=8
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
log3%28x-2%29%2Blog3%28x%2B4%29+=+3 Applying the product rule for logarithms:log%28M%29%2Blog%28N%29+=+log%28%28MN%29%29 we get:
log3%28%28x-2%29%28x%2B4%29%29+=+3 Simplifying:
log3%28x%5E2%2B2x-8%29+=+3 Writing this in exponential form:logb%28x%29+=+y means b%5Ey+=+x
3%5E3+=+x%5E2%2B2x-8 Simplify:
x%5E2%2B2x-17+=+0 Solving by the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
x+=+%28-2%2B-sqrt%282%5E2-4%281%29%28-17%29%29%29%2F2%281%29 Simplifying:
x+=+%28-2%2B-sqrt%2872%29%29%2F2 Simplifying further:
x+=+%28-2%2B-sqrt%2836%2A2%29%29%2F2
x+=+-1%2B3sqrt%282%29 and x+=+-1-3sqrt%282%29
-------------------------------------------------
Solve for x:
e%5Ex+%2B+5+=+8 Subtract 5 from both sides.
e%5Ex+=+3 Take the natural log of both sides.
xln%28e%29+=+ln%283%29 But ln%28e%29+=+1, so:
x+=+ln%283%29
x+=+1.0986 Approx.