SOLUTION: Write equation as a Sum or Difference of logarithms (ln without a base in this question): {{{ln((x^4)sqrt(x^2+1))}}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Write equation as a Sum or Difference of logarithms (ln without a base in this question): {{{ln((x^4)sqrt(x^2+1))}}}      Log On


   

Question 930317: Write equation as a Sum or Difference of logarithms (ln without a base in this question):
ln%28%28x%5E4%29sqrt%28x%5E2%2B1%29%29
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28%28x%5E4%29sqrt%28x%5E2%2B1%29%29

Use the rule ln%28AB%29=ln%28A%29%2Bln%28B%29

ln%28x%5E4%29%22%22%2B%22%22ln%28sqrt%28x%5E2%2B1%29%29%29

Write the square root as the 1%2F2 power



Use the rule ln%28A%5EB%29=B%2Aln%28A%29 on both terms

4ln%28x%29%22%22%2B%22%22expr%281%2F2%29ln%28x%5E2%2B1%29.

[Comment: All logarithms have bases.  It's just that when you see
"log" without a written the base is understood to be 10 and when
you see "ln" without a written base, the base is understood to be
e = 2.718....]

Edwin