NZ Level 8 (NZC) Level 3 (NCEA) [In development]
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Logarithmic Scales

Interactive practice questions

Below is a table of values that shows a log scale relating $x$x and $y$y. Form an equation relating $x$x and $y$y. Express the equation in logarithmic form.

log scale measure ($y$y)   linear measure ($x$x)
$0$0 $=$= $1$1
$1$1 $=$= $10$10
$2$2 $=$= $100$100
$3$3 $=$= $1000$1000
$4$4 $=$= $10000$10000
Approx a minute
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The histogram below shows the area (in km2) for $12$12 countries, plotted using a log scale.

The Richter Scale is a logarithmic scale used to measure the magnitude of an earthquake or tremor. An earthquake that registers $4.0$4.0 on the Richter scale is $10$10 times stronger than an earthquake that measures $3.0$3.0.

How many times stronger is a quake of $7.6$7.6 than one of $5.2$5.2?

Give your answer to the nearest whole number.



Use curve fitting, log modelling, and linear programming techniques


Form and use trigonometric, polynomial, and other non-linear equations


Apply linear programming methods in solving problems


Apply trigonometric methods in solving problems

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