# Math Help - Please solve the equation for "Y"? (a few more problems!)

1. ## Please solve the equation for "Y"? (a few more problems!)

Hello,

I wasn't completly sure on the ones I have solved.

Most of these I have already solved, and have included the answer I got! Please tell me if I have gotten the answer right. Thank you. Some of these I do need a bit of help with.
If you don't have time to do all of them and check them, you can just do a couple! Anything will help! Thank you.

1. (e^-y) + (e^y) = 2

2. (x^2)(ln y) - xlny = 3
I got y = e^(3/(x^2)-x)

3. (ln y )^3 = 5^x
I got e^third root(5x)

4. ln(1+ln y ) = 3
I WASN'T SURE ON THIS ONE. PLEASE HELP! (I didn't know if I was supposed to distribute the "ln" or what. Thank you.

5. (e^(-2y)) + 1 = 3e^x
I got y = (ln3(e^x) - 1)/(-2lne)

6. y^x = lnx + 2
I got y = x root (lnx + 2)

Thank you everyone!

2. $e^{-y} + e^y = 2$

$\frac{1}{e^y} + e^y = 2$

$1 + e^{2y} = 2e^y$ after multiplying both sides by $e^{y}$

$e^{2y} - 2e^y + 1 = 0$

$Y^2 - 2Y + 1 = 0$ if we let $Y = e^y$

$(Y-1)^2 = 0$

$Y-1 = 0$

$Y = 1$

$e^y = 1$

$y = \ln{1}$

$y= 0$.

Hello,

I wasn't completly sure on the ones I have solved.

Most of these I have already solved, and have included the answer I got! Please tell me if I have gotten the answer right. Thank you. Some of these I do need a bit of help with.
If you don't have time to do all of them and check them, you can just do a couple! Anything will help! Thank you.

1. (e^-y) + (e^y) = 2

2. (x^2)(ln y) - xlny = 3
I got y = e^(3/(x^2)-x)

3. (ln y )^3 = 5^x
I got e^third root(5x)

4. ln(1+ln y ) = 3
I WASN'T SURE ON THIS ONE. PLEASE HELP! (I didn't know if I was supposed to distribute the "ln" or what. Thank you.

5. (e^(-2y)) + 1 = 3e^x
I got y = (ln3(e^x) - 1)/(-2lne)

6. y^x = lnx + 2
I got y = x root (lnx + 2)

Thank you everyone!
$\ln{(1 + \ln{y})} = 3$

$1 + \ln{y} = e^3$

$\ln{y} = e^3 - 1$

$y = e^{e^3 - 1}$.

4. The rest (2,3,5 and 6) seem correct to me.

For number 5:

y = (ln3(e^x) - 1)/(-2lne) can be simplified to: y = (ln3(e^x) - 1)/(-2)

Remember ln(e^1) = 1

5. Wow thanks everyone! Hey "Educated", are you from Hastings, Michigan?

6. That's off the topic, but no.

I'm from Hastings, New Zealand. If you go into my profile, you will see.