It is given that n satisfies the equation 2*log(n) - log(5*n - 24) = log(4). Show that n^2 - 20*n + 96 = 0.

Given 2logan - loga(5n-24) = loga(4), we can rearrange to have all the "2logs" on one side and the "logs" on the other.So, 2logan = loga(4) + loga(5n-24). Using the laws of logs (alogn = log(na) and loga + logb = log(a*b)) we get, loga(n2) = loga(4(5n-24)). Since logarithms are a one-to-one function, n2 = 4(5n-24), which rearranges to n2 - 20n + 96 = 0

CS
Answered by Cara S. Maths tutor

5042 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

You're on a game show and have a choice of three boxes, in one box is £10, 000 in the other two are nothing. You pick one box, the host then opens one of the other boxes showing it's empty, should you stick or switch?


Integrate xsin2x


Find the integral of xe^(-2x) between the limits of 0 and 1 with respect to x.


A curve C has equation y = x^2 − 2x − 24x^(1/2) x > 0 find dy/dx


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