SOLUTION: I am looking for how I get the answer for: ln(5x) = 3 + ln(x-1) I move the natural logs to one side to make ln(5x) - ln(x-1) = 3, then use the properties of logarithms to get l

Question 1058775: I am looking for how I get the answer for:
ln(5x) = 3 + ln(x-1)
I move the natural logs to one side to make ln(5x) - ln(x-1) = 3, then use the properties of logarithms to get ln(5x/(x-1)) = 3.
I then make both sides a power of e to cancel out the ln and end up with 5x/(x-1) = e^3
I then multiply both sides by (x-1) to remove the fraction and get 5x = (e^3)x - e^3
Here is where I am stuck. I am unsure how to isolate the x. I know what the answer is supposed to be as this is a practice problem, but I don't know how to get there from here! And maybe I made a mistake in the process. Any help is greatly appreciated! Thank you!
Found 2 solutions by rothauserc, solve_for_x:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
ln(5x/(x-1)) = 3
:
use definition of logarithm
:
5x/(x-1) = e^3
:
note that e = 2.71828
:
5x / (x-1) = (2.71828)^3 = 20.0855
:
5x = 20.0855 * (x-1)
:
5x = 20.0855x - 20.0855
:
15.0855x = 20.0855
:
**********
x = 1.3314
**********
:

Answer by solve_for_x(190) (Show Source): You can put this solution on YOUR website!
What you have is correct so far.

From here:

5x = (e^3)x - e^3

rearrange the equation by adding e^3 to both sides, and subtracting
5x from both sides. This gives:

(e^3)x - 5x = e^3

Factor the left side to get:

(e^3 - 5)x = e^3

Finally, divide both sides by (e^3 - 5) to get:

If desired, this can be simplified as:

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