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We then use the rules of logarithms to simplify the expression. First use log(ab) = log a + log b We can now use log a k = k log a to get rid of the powers. Expand the brackets and collect the terms containing x on one side. Use the rules of logarithms to write the solution in the correct form: logl og log logl og log ab l b ab l a b b = b ...
There are three laws of logarithms which you must know. log a x + log a y = log a ( xy ) where a , x , y > 0 . If two logarithmic terms with the same base number (a above) are being added together, then the terms can be combined by multiplying the arguments (x and y above). log 5 4 ) 2 × 4 = log 5 8. where a , x , y > 0 .
Example 1: Use Logarithm Rules Expand using logarithm rules until no more can be applied. We see that the argument is first and foremost a product. Therefore, we will use the Product Rule first. There are also some exponents. Please observe that can be written as . Therefore, we can write the following:
All of the following are exponential functions except: 2. The point (-3, n) exists on the exponential graph shown. The value of n is: 3. The graph of. 4. The point (-5, n) exists on the exponential graph shown. If the function has the form y = abx + k, the value of n is: 5. If the graph of is stretched vertically so it passes through the point , 9.
Example 1: Simplify 4 5∙9 −12 4 Example 2: Simplify 2 ∙9 ∙3 2 Example 3: Simplify each expression without negative exponents. a. 4∙2 −3 3 2 b. −4 ∙7 ∙2 2 c. (2 3 −3)(2 −1 3) d. (4 3 2)(3 −4 −5) RULES OF EXPONENTS Multiplying Powers with the Same Base
Question 1 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
EXPONENT RULES & PRACTICE 1. PRODUCT RULE: To multiply when two bases are the same, write the base and ADD the exponents. Examples: A. B. C. 2. QUOTIENT RULE: To divide when two bases are the same, write the base and SUBTRACT the exponents. Examples: A. B. ˘ C. ˇ ˇ 3.
