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Given that log 2 = x, log 3 = y and log 7 = z, express the following expressions in terms of x, y, and z. (1) log 12 (2) log 200. 14. (3) log (4) log 0:3. 3. (5) log 1:5 (6) log 10:5 6000. (7) log 15 (8) log. 7.
we need to have some understanding of the way in which logs and exponentials work. De nition: If x and b are positive numbers and b 6= 1 then the logarithm of x to the base b is the power to which b must be raised to equal x. It is written logb x. In algebraic terms this means that if y = logb x then x = by
Enjoy these free sheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key. Logarithmic Equations Worksheet. Properties of Logarithms Worksheet (mixed worksheet on all 3 properties below)
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com
Example 1. Expand log2493 . log2493 = 3 • log249 . The answer is 3 • log249. Use the Power Rule for Logarithms. Example 2. Expand log3(7a) log3(7a) = log3(7 • a) = log37 + log3a. The answer is log37 + log3a. Since 7a is the product of 7 and a, you can write 7a as 7 • a. Use the Product Rule for Logarithms. Example 3. 11 . Expand log. .
Free 29 question Worksheet (pdf) with answer key on the properties of logarithms (product,quotient and power rules)
Simplify each of the following logarithmic expressions, giving the final answer as a single logarithm. a) log 7 log 22 2+ b) log 20 log 42 2− c) 3log 2 log 85 5+ d) 2log 8 5log 26 6− e) log 8 log 5 log 0.510 10 10+ − log 142, log 52, log 645, log 26, log 8010
