# Confirmation of exponential equation answers

• Sep 1st 2011, 09:22 AM
crazycarlos61
I did a couple of problems and am just asking if someone could check them for me to see if I got them right.

Solve for y in terms of t:
Ln(50-3y)=.5t+ln(5)

I got : y=(5e^(.5)-50)/-3
I think I got close but I'm not sure if I have it right

Ln(10-y)=2t+ln8
I got : y=-8e^2t +10
• Sep 1st 2011, 09:29 AM
Siron
Re: Confirmation of exponential equation answers
First one is fine, but try to simplify as much as possible:
$\ln(50-3y)=\frac{1}{2}t+\ln(5)$
$\Leftrightarrow e^{\frac{1}{2}+\ln(5)}=50-3y$
$\Leftrightarrow y=\frac{50-e^{\frac{1}{2}+\ln(5)}}{3}$
$\Leftrightarrow y=\frac{50}{3}-\frac{\sqrt{e}\cdot 5}{3}$
$\Leftrightarrow y=\frac{5}{3}\left(10-\sqrt{e}\right)$

Second one is fine!

$\ln(10-y)=2t+\ln(8)$
$\Leftrightarrow \ln(10-y)=\ln(e^{2t})+\ln(8)$
$\Leftrightarrow \ln(10-y)=\ln(e^{2t}\cdot 8)$
$\Leftrightarrow 10-y=e^{2t}\cdot 8$
$\Leftrightarrow y=10-e^{2t}\cdot 8$
• Sep 1st 2011, 09:35 AM
crazycarlos61
Re: Confirmation of exponential equation answers
Thanks once again.
• Sep 1st 2011, 09:40 AM
Siron
Re: Confirmation of exponential equation answers
You're welcome, again! :D