SOLUTION: The problem is: 5+ ln x^2 = 4 I have absolutely no clue how to solve this problem. Please and thank you in advance.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The problem is: 5+ ln x^2 = 4 I have absolutely no clue how to solve this problem. Please and thank you in advance.      Log On


   

Question 108808: The problem is:
5+ ln x^2 = 4
I have absolutely no clue how to solve this problem.
Please and thank you in advance.
Found 2 solutions by Fombitz, Earlsdon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Knowns on one side. Unknowns on the other.
5%2B+ln%28x%5E2%29+=+4
5-5%2B+ln%28x%5E2%29+=+4-5Subtract 5 from both sides.
ln%28x%5E2%29+=+-1
x%5E2+=+e%5E%28-1%29Exponentiate both side.
sqrt%28x%5E2%29+=+sqrt%28e%5E%28-1%29%29Take the square root of both sides.
x+=+sqrt%28e%5E%28-1%29%29 and x+=+-sqrt%28e%5E%28-1%29%29 Find positive and negative root.
Two solution x=0.606 and x=-0.606.
Check your answers
5%2B+ln%28x%5E2%29+=+4
5%2B+ln%28.606%5E2%29+=+4
5%2B+ln%28.368%29+=+4
5%2B+%28-1.0%29=+4
4=4
True statement.
Good answers.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
5%2Bln%28x%5E2%29+=+4 First, subtract 5 from both sides.
ln%28x%5E2%29+=+-1 Now apply the power rule to the logarithm. log%28x%5En%29+=+nlog%28x%29
2%2Aln%28x%29+=+-1 Divide both sides by 2.
ln%28x%29+=+-%281%2F2%29 Now rewrite the logarithm in exponential form: If Log%5Bb%5D%28x%29+=+y, then y%5Eb+=+x
e%5E%28-1%2F2%29+=+x Simplify:
x+=+1%2Fsqrt%28e%29