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

3.1.1.6

identify contexts suitable for modelling by logarithmic functions and use them to solve practical problems; verify and evaluate the usefulness of the model using qualitative statements and quantitative analysis

3.2.2.4

use logarithmic functions and their derivatives to solve practical problems

3.3.3.1

calculate the area under a curve

3.3.3.3

calculate the area between curves with and without technology

What is Mathspace

About Mathspace