Question

ln(5+4x)-ln(3+x)=ln3

Answer 1

ln(x)-ln(y)=ln(x/y)

Answer 2

Write ln[(5+4x)/{3+x)]=ln3

Answer 3

base e both sides to get rid of the natural logs

Answer 4

[(5+4x)/(3+x)]=3

Answer 5

Solve for x

Answer 6

5+4x=3(3+x) I multiply 3+x on both sides

Answer 7

5+4x=9+3x Distributive property

Answer 8

5+x=9 so x=9-5=4

Answer 9

Always check your solution when working with log. You never know the solution may not be in the domain

Answer 10

thank you for your help

Answer 11

In this case it is, because 5+4x and 3+x is positive for x=4

Answer 12

no problem

Answer 13

I have one more question. Is that ok?

Answer 14

Go ahead

Answer 15

r=p-k ln t, for t

Answer 16

So we want to solve for t. First get the ln(t) by itself

Answer 17

Subtract p on both sides: r-p=-klnt

Answer 18

Now divide -k on both sides: (r-p)/(-k)=lnt

Answer 19

Base e both sides to get ride of the natural log

Answer 20

e^[-(r-p)/k]=t