Question

Find x and y such that : lnx.lny=6 and xy=e^5.

Answer 1

from the first equation lnx =6/ln y------------(1)
taking ln for the second equation
ln x +ln y =5
substituting (1) in the above equation
you get , (6/ln y) + ln y = 5
solve for ln y and substitute the ans into the first equation and get the value of ln x
and then take anti log

Answer 2

(lnx)(lny) = 6
xy = e^5
This means ln(xy) = ln(e^5)
ln(xy) = 5
lnx + lny = 5. (one of the laws of logarithms)
Let w = lnx and v = lny, then the 2 equations become:
wv = 6
w + v = 5.
Those are easy to solve for w and v.
Once you have w and v you can find x and y using
w = lnx means e^w = x
v = lny means e^v = y

Answer 3

got it!!!

Answer 4

Ok ! Good solution.

Answer 5

I type fast. I didn't mean to scoop DHASHNI.

Answer 6

what???

Answer 7

You were answering when I started to answer and I finished first, which was sort of rude and I didn't mean to be rude. That's all.

Answer 8

k!!!