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8. Prove the following statements. (1) logp b x = 2log x (2) log p1 b p x = log x (3) log 4 x2 = log p x 9. Given that log2 = x, log3 = y and log7 = z, express the following expressions
Simplify each of the following logarithmic expressions, giving the final answer as a number not involving a logarithm. a) log 4 log 0.52 2− b) log 10 log 52 2− c) 2log 4 log 82 2+ d) 2log 5 2log 0.2520 20− e) 3log 8 3log 324 24+ 3 , 1 , 7 , 2 , 3
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)
•explain what is meant by a logarithm •state and use the laws of logarithms •solve simple equations requiring the use of logarithms. Contents 1. Introduction 2 2. Why do we study logarithms ? 2 3. What is a logarithm ? if x = an then log a x = n 3 4. Exercises 4 5. The first law of logarithms log a xy = log a x+log a y 4 6. The second ...
Rules of Logarithms. loga x = y () ay = x. aloga M = M. loga a = 1. log 1 = 0. loga Mr = r loga M. log a(M N) = log M + log. N. log a(M ) = log M.
Free 29 question Worksheet (pdf) with answer key on the properties of logarithms (product,quotient and power rules)
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. .
