Which Real values of x satisfy 3/ln(x) = ln(x) + 2?

The problem with this equation lies with the denominator on the left hand side. If we recall our graph of ln(x) however, we know that ln(x) is always positive and not equal to 0. Now we can safely multiply it up. The equation now reads:3 = (ln(x))2 + 2ln(x)We can recognise this as a quadratic equation in ln(x), and factorise it as such:(ln(x)+3)(ln(x)-1) = 0from which we deduce the solutions exist where ln(x) is equal to 1 or -3, the latter of which does not exist for any real values. Hence we consider ln(x) = 1, which is achieved when x = e, our one and only real solution. (note that we can confirm this solution by substituting x = e into the original equation).

Answered by Mark H. Maths tutor

3914 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve y = 2x^3 - ax^2 + 8x + 2 passes through the point B where x=4. Given that B is a stationary point of the curve, find the value of the constant a.


The curve with the equation: y=x^2 - 32sqrt(x) + 20 has a stationary point P. Find the coordinates of P.


Polynomial long division, how do I do it?


Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences