SOLUTION: If ln a=2, ln b=3, and ln c=5, evaluate the following: In square root a^3 b^2 c^1

Algebra ->  Equations -> SOLUTION: If ln a=2, ln b=3, and ln c=5, evaluate the following: In square root a^3 b^2 c^1       Log On


   

Question 1132218: If ln a=2, ln b=3, and ln c=5, evaluate the following:

In square root a^3 b^2 c^1
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

If ln%28a%29=2, ln+%28b%29=3, and ln+%28c%29=5, evaluate the following:

ln%28a%29=2 =>a+=+e%5E2
ln+%28b%29=3=>b+=+e%5E3
ln+%28c%29=5=>c+=+e%5E5

sqrt%28a%5E3%2A+b%5E2%2A+c%5E1%29=sqrt%28%28e%5E2%29%5E3%2A+%28e%5E3%29%5E2%2A+e%5E5%29+

sqrt%28a%5E3%2A+b%5E2%2A+c%5E1%29=e%5E3%2Ae%5E3%2Ae%5E2%2Asqrt%28e%29+
sqrt%28a%5E3%2A+b%5E2%2A+c%5E1%29=e%5E8%2Asqrt%28e%29+
approximately:4914.768840



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
If ln a=2, ln b=3, and ln c=5, evaluate the following:

In square root a^3 b^2 c^1 


Assuming In square root a^3 b^2 c^1 is ACTUALLY ln%28sqrt%28a%5E3b%5E2c%5E1%29%29, we get:

ln+%28sqrt%28a%5E3b%5E2c%29%29 =====> ln+%28a%5E3%29%5E%281%2F2%29%28b%5E2%29%5E%281%2F2%29c%5E%281%2F2%29 ======> matrix%282%2C1%2C+%22+%22%2C+ln+%28a%5E%283%2F2%29b%5E%282%2F2%29c%5E%281%2F2%29%29%29 =====>  =====> %283%2F2%29+%2A+ln+%28a%29+%2B+ln+%28b%29+%2B+%281%2F2%29+%2A+ln+%28c%29

Substituting 2 for ln (a), 3 for ln (b), and 5 for ln (c), we get:  <==== Correct answer