FP3 - Hyperbolic Functions

Given that artanhx - artanh y = ln5, find y in terms of x

I have no idea where to start, i turned artanh x and y into 1/2n(1+x/1-x) for both of them but i cant work out to go after there, can anyone help?

Original post by Jowen07

Given that artanhx - artanh y = ln5, find y in terms of x

I have no idea where to start, i turned artanh x and y into 1/2n(1+x/1-x) for both of them but i cant work out to go after there, can anyone help?

What do you know about the addition and subtraction of logarithms?

OP

I then get to 1+x/1-x = 10+10y/1-y, cant go further

for the x term, for example, use the logarithmic version of arctanh(x), i.e:

\displaystyle arctanh(x)= \frac{1}{2} ln (\frac{1+x}{1-x})

do the same with the y term, combine the terms using the laws of logs, exponentiate, and use some algebraic manipulation.

Original post by Jowen07

I then get to 1+x/1-x = 10+10y/1-y, cant go further

multiply both sides by (1-x)(1-y) and collect like terms.

Quick Reply

Latest

Trending

Trending

Articles for you

Powerful questions business students forget to ask their career advisers

Powerful questions business students forget to ask their career advisers

How to revise for A-level Maths exams: AQA explains what to do

How to revise for A-level Maths exams: AQA explains what to do

What jobs could you do with a degree in policing?

What jobs could you do with a degree in policing?

How technology is transforming education

How technology is transforming education