Question

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

Answer 1

what?

Answer 2

First isolate \(\ln t\)

Answer 3

Can you do that?

Answer 4

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?

Answer 5

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

Answer 6

Suppose you let \(\ln t = x\). Can you solve for \(x\)?\[
r=p-kx
\]

Answer 7

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

Answer 8

Hello?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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