Use logarithms to solve the equation 2^(n-3) = 18000, giving your answer correct to 3 significant figures.

To find the answer first you have to take a log of both sides.

I am going to use log to the base 2 for my example - but any base will work as long as they are the same on both sides of the equals sign 

log(2n-3)=log(18000)

Using the rules of logerithms you can bring down the power

(n-3)log(2)=log(18000)

As I am using base 2 log(2)=1

n-3=log(18000)

n=log(18000)+3

n=17.1

EJ
Answered by Emily J. Maths tutor

6826 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you prove that (3^n)-1 is always a multiple of 2?


The equation (t – 1)x^2 + 4x + (t – 5) = 0, where t is a constant has no real roots. Show that t satisfies t2–6t+1>0


Curve C has equation x^2 - 3xy - 4y^2 + 64 = 0. a) find dy/dx in terms of x and y. b) find coordinates where dy/dx=0.


Express x^2-4x+9 in the form (x-p)^2+q where p and q are integers


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning