SOLUTION: solve for x: 4=ln&#8730;(x-2) +2 i can get 2=ln&#8730;(x-2) but im not sure what to do after that. Please help thank you in advance. :) <3

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: solve for x: 4=ln&#8730;(x-2) +2 i can get 2=ln&#8730;(x-2) but im not sure what to do after that. Please help thank you in advance. :) <3       Log On

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Question 65919: solve for x: 4=ln√(x-2) +2
i can get 2=ln√(x-2) but im not sure what to do after that. Please help thank you in advance. :) <3

Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
4+=+ln%28sqrt%28x-2%29%29%2B2 Subtract 2 from both sides.
2+=+ln%28sqrt%28x-2%29%29 Rewrite the right side in exponential form.
2+=+ln%28x-2%29%5E%281%2F2%29 Apply the power rule for logarithms.
2+=+%281%2F2%29ln%28x-2%29 Multiply both sides by 2.
ln%28x-2%29+=+4 Rewrite this in exponential form.
x-2+=+e%5E4 Add 2 to both sides.
x+=+e%5E4%2B2 Evaluate.
x+=+54.5982%2B2
x+=+56.5982 Approximately.
Check:
4+=+ln%28sqrt%2856.5982+-+2%29%29%2B2
4+=+ln%28sqrt%2854.5982%29%29%2B2 Use your calculator to evaluate.
4+=+2.0000%2B2
4+=+4