The properties on the left hold for any base a. The properties on the right are restatements of the general properties for the natural logarithm. Many logarithmic expressions may be rewritten, either expanded or condensed, using the three properties above. Expanding is breaking down a complicated expression into simpler components.
Polaris Side by Side ATV Prices. One of the most popular ATV manufacturers is Polaris. They manufacture an entire line of ATVs that range in price from around $8,000 for the Ranger 400 to close to $15,000 for some of the Ranger 800 series.
Follow the stars of the Big Dipper from the handle to the side of the bowl, to the bowl bottom, and up the other side; the two stars forming the second side, Dubhe and Merak, point to Polaris. Take the distance between Dubhe and Merak; Polaris is the bright star that sits about five times that distance away.