Solving following equation for y?

Question

hi,

i would like to find out how to solve this problem

i would like to find out (for those values of x for which a solution exists), i would like to find out how to solve the following equation for y
2 e^4 y-10 = 5 x^2 (2 e to the power of 4y-10 equals 5 x squared)

thanks for your help.

i would like to know what y equals to be more precise

Answer 1

2e^(4y-10)=5x^2
e^(4y-10) =2.5 x^2
ln e^(4y-10) =ln 2.5x^2
4y-10 = ln 2.5x^2
4y = 10 + ln2.5x^2
y = 2.5 + .25 ln2.5x^2
y = 2.5 ln2.5x^.5

Answer 2

first divide by 2 so you have e^(4y-10)=5/2x^2
next, take the natural log of both sides
so you have lne^(4y-10)=ln5/2x^2
the ln of e sort of cancels out so you actually have
4y-10=ln5/2x^2
add 10 to both sides
4y=ln5/2x^2 + 10
then divide both by 4
y=ln5/2x^2 + 10 all over four

voila!

Answer 3

2e^(4y-10)=5x^2
e^(4y-10) =2.5 x^2
ln e^(4y-10) =ln 2.5x^2
4y-10 = ln 2.5x^2
4y = 10 + ln2.5x^2
y = 2.5 + .25 ln2.5x^2
y = 2.5 ln2.5x^.5