Converting
Converting
Log Scale Graphs
Order of Magnitude
100
Given that
log(x)=2
Find the value of x
x=100
100
Given that
log(x) = 4.5
Find the value of x, correct to 2 decimal places
x=31622.78
100
The histogram below shows the distribution of brain weights (in grams) of 27 animal species plotted on a log scale.
The brain weight of a mouse is 0.4g. What value would be plotted on the log scale (round to 1 decimal place)
log(0.4)=-0.39794
-0.4
100
Determine the order of magnitude of 4500
log(4500) = 3.653
Order of magnitude is 3
200
The brightness of a star (B) is measured using a logarithmic scale. The logarithmic brightness of a star is recorded as 3.25
Given that:
log(B)=3.25
Determine the actual brightness, correct to 2 decimal places.
B=10^3.25
B=1778.28
200
The distance between two planets is recorded as 100,000km.
Calculate the logarithmic value of this distance.
log(100,000)=5
5
200
The histogram below shows the distribution of brain weights (in grams) of 27 animal species plotted on a log scale.
The brain weight of an African elepaht is 5712g. What is the log of this brain weight (to two significant figures)?
log(5712) = 3.756788
3.8
200
The distance between two cities is
3.85*10^6
Determine the order of magnitude of this distance.
Order of magnitude is 6
300
The population of a particular insect species is represented by a logarithmic value of 4.
Determine the actual population
log(P)=4
P=10^4
P=10000
300
A microscopc organism has a length of 0.0000356 metres.
Calculate the logarithmic value of its length, round to 3 decimal places.
log(0.0000356)=-4.44855
-4.449
300
The histogram below shows the distribution of brain weights (in grams) of 27 animal species plotted on a log scale.
What brain weight (in grams) is represented by the number 2 on the log scale?
10^2 = 100
100 grams
300
Determine the order of magnitude of 0.00072
log(0.00072)=-3.14
Order of magnitude is -3
400
The intensity of an earthquake is measured using a logarithmic scale. An earthquake has an actual amplitude ratio of 850,000.
Calculate the logarithmic value of the amplitude ratio, to 3 significant figures
log(850,000)=5.929418
5.93
400
The intensity of an earthquake is measured using a logarithmic scale. An earthquake has an logarithmic amplitude ratio of 7.2
Calculate the actual value of the amplitude ratio, to 3 significant figures.
10^7.2=15848931.9246
15,800,000
400
The histogram below shows the distribution of brain weights (in grams) of 27 animal species plotted on a log scale.
Use the histogram, to determine the number of these animals with brain weights of 1000grams or more.
log(1000) = 3
3 or more = 5 animals
400
The mass of a large aircraft is approximately
2.75*10^5
The mass of a submarine is approximately
3.2*10^3
Which object is heavier? Justify with calculations.
Order of magnitude of aircraft is 5, whilst order of magnitude of submarine is 3.
Therefore the aircraft is approximately 2 order of magnitudes heavier (aka. 100 times heavier!)
OR calculate actual values: 275,000kg > 3,200 kg. Therefore aircraft is heavier.
500
The intensity of a sound is measured using a logarithmic scale. A particular sound has a logarithmic intensity value of 5.85.
Given that:
log(I)=5.85
Determine the actual sound intensity, correct to 3 significant figures in scientific notation.
I=10^5.85
707945.7843
708000 (3sf)
I=7.08*10^5
500
The concentration of a chemical in a water sample is recorded using a logarithmic scale. It's logarithmic concentration is measured as -4.68
Determine the actual concentration, rounding to 3 significant figures and in scientific notation.
log(C)=-4.68
C=10^-4.68
0.000020892961
0.0000209 (3 sf)
2.09*10^-5
500
The histogram below shows the distribution of brain weights (in grams) of 27 animal species plotted on a log scale.
Use the histogram to calculate the percentage of animals that weigh from 1 gram to less than 100 grams, rounded to the nearest whole percentage.
log(1)=0
log(100)=2
Between 0 and 2 = 4 + 8
12 animals
12 out of 27 = 12/27 *100
44%
500
The diameter of grain of sand is approximately
7.5*10^-4
The diameter of a humain hair is
2.8*10^-4
Which object has a larger diameter. Justify your response.
Since they have the same order of magnitude, just compare the numbers.
Since 7.5>2.8, therefore the sand has a larger diameter