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 |
The histogram below shows the area (in km^{2}) 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.