r=p-k ln t, solve for t
can someone please explain how ln becomes e? thanks!

Question

r=p-k ln t, solve for t
can someone please explain how ln becomes e? thanks!

anonymous · Answer

what?

anonymous · Answer

First isolate $\ln t$

anonymous · Answer

Can you do that?

anonymous · Answer

when I enter r=p-klnt in my Mathway app, the answer comes with t=e^[(p-r)/k]
but how does the ln t become e?

anonymous · Answer

Hey, can you solve for $\ln t$ first?  Then I can explain.

anonymous · Answer

Suppose you let $\ln t = x$.  Can you solve for $x$?$$
r=p-kx
$$

anonymous · Answer

Yes or no? I'm running out of time.

anonymous · Answer

Hello?

anonymous · Answer

So you can't even do basic algebra?  Is that how I am supposed to interpret your silence?

anonymous · Answer

Okay all I can really tell you is that $$
b^a=c\iff \log_{b}(c)=a
$$

anonymous · Answer

If we let $b=e$, then $\log_3(c) = \ln(c)$.$$
e^a=c\iff \ln(c)=a
$$

anonymous · Answer

If you let $c=t$, then we can see that $$
e^a=t\iff \ln(t) =a
$$

anonymous · Answer

Finally, let $a$ be whatever you got when you solved for $\ln(t)$.

anonymous · Answer

sorry for not replying quicker...thanks for your help!