topic badge
CanadaON
Grade 12

Applications of logs I

Interactive practice questions

As elevation ($A$A metres) increases, atmospheric air pressure ($P$P pascals) decreases according to the equation $A=15200\left(5-\log P\right)$A=15200(5logP).

Trekkers are attempting to reach the $8850$8850 m elevation of Mt Everest’s summit. When they set up camp at night, their barometer shows a reading of $45611$45611 pascals. How many more vertical metres do they need to ascend to reach the summit?

Give your answer to the nearest metre.

Easy
3min

The Palermo impact hazard scale is used to rate the potential for collision of an object near Earth. The hazard rating $P$P is given by the equation $P=\log R$P=logR, where $R$R represents the relative risk of collision.

Two asteroids are identified as having a relative risk of collision of $\frac{6}{7}$67 and $\frac{4}{5}$45 respectively.

Easy
3min

pH is a measure of how acidic or alkaline a substance is, and the pH scale goes from $0$0 to $14$14, $0$0 being most acidic and $14$14 being most alkaline. Water in a stream has a neutral pH of about $7$7. The pH $\left(p\right)$(p) of a substance can be found according to the formula $p=-\log_{10}h$p=log10h, where $h$h is the substance’s hydrogen ion concentration.

Medium
4min

The spread of a virus through a city is modelled by the function $N=\frac{15000}{1+100e^{-0.5t}}$N=150001+100e0.5t, where $N$N is the number of people infected by the virus after $t$t days.

Medium
5min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

Outcomes

12F.A.2.4

Pose problems based on real-world applications of exponential and logarithmic functions and solve these and other such problems by using a given graph or a graph generated with technology from a table of values or from its equation

12F.A.3.4

Solve problems involving exponential and logarithmic equations algebraically, including problems arising from real-world applications

What is Mathspace

About Mathspace