SOLUTION: evaluete Logx(x+3)=4

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Question 378051: evaluete
Logx(x+3)=4
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Not sure if you meant log%28x%2C%28x%2B3%29%29=4 or log%28%28x%28x%2B3%29%29%29=4???
I'll work it both ways.
log%28x%2C%28x%2B3%29%29=4
x%5E4=x%2B3
x%5E4-x-3=0
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graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C0%2Cx%5E4-x-3%29
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Using Newton's method to find the positive solution,
f=x%5E4-x-3
df%2Fdx=4x%5E3-1
x%5B1%5D=2
highlight%28x=1.452627%29
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log%28%28x%28x%2B3%29%29%29=4
x%28x%2B3%29=10%5E4
x%5E2%2B3x+=10000
x%5E2%2B3x%2B9%2F4=10000%2B9%2F4
%28x%2B3%2F2%29%5E2=40009%2F4
x%2B3%2F2=0+%2B-+sqrt%2840009%29%2F2
x=-3%2F2+%2B-+sqrt%2840009%29%2F2
highlight%28x=%28-3+%2B-+sqrt%2840009%29%29%2F2%29