Solve the Equation: 2ln(x)−ln (7x)=1

This is an equation laid out in terms of the natural logarithm, which essentially is the reverse function of ex . From this equation we need to find a solution for x =? Since we know that this equation involves logarithms, we should keep the logarithm laws in mind, which are;
eln(x)= xln(a) + ln(b) = ln(ab)aln(b) = ln(ab)
1) Firstly we should change the first term of the equation, using the logarithm laws 3rd logarithm law from above, so that 2ln(x) = ln(x2) 2) Combine all the terms on the left hand side of the equation to form one term, using the 2nd log law to give you : ln(x2/7x) = 13) Now we can undo the natural logarithm to give us an equation in terms of x, using the 1st log law stated above. Therefore x2/7x = e14) We can now rearrange this equation and factorise it to find solutions of x:x2=e
7x (by multiplying across by 7x)x2-7ex=0 (subtracting 7ex from both sides)x(x-7e)=0 (factorising)Therefore --> x=0 or x =7e


DG
Answered by Dhruv G. Maths tutor

5683 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A quantity N is increasing with respect to time, t. It is increasing in such a way that N = ae^(bt) where a and b are constants. Given when t = 0, N = 20, and t = 8, N = 60, find the value: of a and b, and of dN/dt when t = 12


Find all solutions to the trig equation 2sin(x)^2 + 3sin(x) - 2 = 0 in the range 0 <= x <= 360 degrees


x = 3t - 4, y = 5 - (6/t), t > 0, find "dy/dx" in terms of t


Let f(x)= x^3 -9x^2 -81x + 12. Calculate f'(x) and f''(x). Use f'(x) to calculate the x-values of the stationary points of this function.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences