Help me check my answer? Logarithmic question

[qwert]

Question:

Given that lnx=m and lny=n ,
express ln(e√(x/y)) in terms of m and n.

My working:
ln(e√(x/y))
=lne + ln√(x/y)
=lne + ln√x - ln√y
=1 + lnx^1/2 - lny^1/2
= 1 + 1/2lnx - 1/2lny
=1 +1/2m - 1/2 n

Am i correct? Thank you! If not what is the correct way?

 

[MarkFL]

Looks good!

 

[qwert]

Just the affirmation i needed!
Thank you!

 

[HallsofIvy]

Confirmation: That is \(\displaystyle e(\sqrt{x/y})\), not \(\displaystyle e^{\sqrt{x/y}}\)?

 

[Deleted member 4993]

Question:

Given that lnx=m and lny=n ,
express ln(e√(x/y)) in terms of m and n.

My working:
ln(e√(x/y))
=lne + ln√(x/y)
=lne + ln√x - ln√y
=1 + lnx^1/2 - lny^1/2
= 1 + 1/2lnx - 1/2lny
=1 +1/2m - 1/2 n

Am i correct? Thank you! If not what is the correct way?

You are correct if your problem IS:

\(\displaystyle \displaystyle ln\left [e \ * \ \sqrt\frac{x}{y}\right ]\)

and NOT:

\(\displaystyle \displaystyle ln\left [e^{\sqrt\frac{x}{y}}\right ]\) or

\(\displaystyle \displaystyle ln_e\left (\sqrt\frac{x}{y}\right )\)

 

[Deleted member 4993]

Why is "or" not in capitals?

Ran out of red ink - capitals take more ink!!