You are Here: Home >< Maths

two questions about 'ln' on C3 watch

1. When I get an equation of 'f(x)= ln(2+3x)', how do I derive it from the original equation of 'ln x'.

Am I right in thinking that to get from 'ln x' to 'f(x)= ln(2+3x)', I divide the x values of 'ln x' by three, and then shift the whole curve 2 units to the left ? Also, where would the asymtote be in 'f(x)= ln(2+3x)'?

my other question is, when find I was finding the inverse of 'ln(5x-2)', I got: 'e^(x+5) / 5'. But in the answers, it has exponential just to the power of 'x', whereas I thought it would be to the power of 'x+5'. Can someone explain this for me?
2. (Original post by W.H.T)
When I get an equation of 'f(x)= ln(2+3x)', how do I derive it from the original equation of 'ln x'.

Am I right in thinking that to get from 'ln x' to 'f(x)= ln(2+3x)', I divide the x values of 'ln x' by three, and then shift the whole curve 2 units to the left ? Also, where would the asymtote be in 'f(x)= ln(2+3x)'?

my other question is, when find I was finding the inverse of 'ln(5x-2)', I got: 'e^(x+5) / 5'. But in the answers, it has exponential just to the power of 'x', whereas I thought it would be to the power of 'x+5'. Can someone explain this for me?
Yes, remember, stretches and reflections first, translations last. The asymptote would be when x = -2/3 because that makes the equation ln0 which is undefined.

For the inverse of ln(5x-2)
The steps are simple so I might as well just show you:

y = ln(5x-2)
x = ln(5y-2)
e^x = 5y - 2

5y = e^x + 2
y = (e^x +2)/5
3. 1. yup u r right, the asymtote will be at -2/3 i think

2. I got the inverse as (e^x + 2)/5 if its right than I can explain

Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 16, 2010
The home of Results and Clearing

1,377

people online now

1,567,000

students helped last year
Today on TSR

University open days

1. Sheffield Hallam University
Tue, 21 Aug '18
2. Bournemouth University
Wed, 22 Aug '18
3. University of Buckingham
Thu, 23 Aug '18
Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants