# Thread: Solve equation for t?

1. ## Solve equation for t?

How do you solve this equation for t using logs and base "a"? I can't figure it out. There are also options, but I can't work it out to anything that looks close to one of them. (Also, this is for an online practice thing that quizzes us but only gives participation points, so it's not worth anything, but it doesn't show right and wrong answers after so I won't even know what I got wrong)

2. ## Re: Solve equation for t?

$\large C=Ba^{\frac{t}{D}}-K$

$\large C+K=Ba^{\frac{t}{D}}$

$\large \dfrac{C+K}{B}=a^{\frac{t}{D}}$

$\large \log_a\left(\dfrac{C+K}{B}\right)=\dfrac{t}{D}$

$\large t=D\log_a\left(\dfrac{C+K}{B}\right)$

3. ## Re: Solve equation for t?

Originally Posted by romsek
$\large C=Ba^{\frac{t}{D}}-K$

$\large C+K=Ba^{\frac{t}{D}}$

$\large \dfrac{C+K}{B}=a^{\frac{t}{D}}$

$\large \log_a\left(\dfrac{C+K}{B}\right)=\dfrac{t}{D}$

$\large t=D\log_a\left(\dfrac{C+K}{B}\right)$
Thank you! I always make mistakes with this kind of thing and end up off!