topic badge

6.09 Further applications of logarithms

Interactive practice questions

Solve $v=u-a\ln t$v=ualnt for $t$t.

Easy
2min

Solve $r=\frac{u}{\ln t}-b$r=ulntb for $t$t.

Medium
2min

Bart releases his new book on the $6$6th of January. The number of sales of the book per day since its release is displayed in the graph below.

From the first day of release onwards, the book enjoys a steady growth in sales.This growth is roughly modelled by the equation:

$f\left(t\right)=1483+93\ln t$f(t)=1483+93lnt

where $t$t is the number of days since the book's release.

Easy
1min

Beth uploads a new video to her popular website.

The number of people viewing the video (in thousands) is roughly modelled by the equation:

$V=-180+57\ln x$V=180+57lnx

where $x$x is the number of minutes since the video was upload.

The following table shows the number of people who have viewed the video (in thousands) at certain intervals (in minutes) since she completed the upload.

Medium
4min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

Outcomes

ACMMM126

recognise the definite integral ∫ {from a to b} f(x)dx as a limit of sums of the form ∑_i f(x_i) δx_i

ACMMM132

calculate the area under a curve

ACMMM134

calculate the area between curves in simple cases

ACMMM155

solve equations involving indices using logarithms

ACMMM158

identify contexts suitable for modelling by logarithmic functions and use them to solve practical problems

ACMMM163

use logarithmic functions and their derivatives to solve practical problems

What is Mathspace

About Mathspace