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.
Sling TV adds TCM, game channel Polaris+. For those keeping track, Sling TV added its 23rd channel to its basic plan, which costs $20 a month. But itâs an unusual choice: Maker Studiosâ Polaris+, a channel focusing on the video-gaming industry. The rest of the lineup is familiar and traditional pay-TV brands, like ESPN, HGTV and the Disney Channel.