# Log Properties. Because logs are REALLY exponents they have similar properties to exponents. Recall that when we MULTIPLY like bases we ADD the exponents.

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Log Properties

Because logs are REALLY exponents they have similar properties to exponents. Recall that when we MULTIPLY like bases we ADD the exponents. (Simplify (3 2 )(3 10 ) And when we DIVIDE like bases we SUBTRACT the exponents. (Simplify (3 2 )(3 10 ) Something similar happens with logs…. (And of course, whatever holds for logs also holds for ln.

Example 1: Product Property If a product is being “logged” we can change it into a sum. log 3 40 40 is a can be a lot of different products. For example: 4 and 10 or 8 and 5. They tell you what to factor it into.

Example 1: Product Power log 6 40 For example: Use log 6 5 =.898 and log 6 8 = 1.161 to evaluate. log 3 40 So we rewrite: log 6 40 into log 6 (5)(8) = log 6 5 + log 6 8 We know the values of the yellow portion so we replace it with.898 + 1.161 The value is 2.059

Example 2: Product Property If a product is being “logged” we can change it into a sum. log 5 5x So we rewrite: log 5 5x into log 5 (5)(x) = log 5 5 + log 5 x

Example 3: Quotient Property If a quotient is being “logged” we can change it into a difference. For example: Use log 6 5 =.898 and log 6 8 = 1.161 to evaluate We rewrite as follows :

Example 3: For example: Use log 6 5 =.898 and log 6 8 = 1.161 to evaluate The value is -0.263

Example 4: Power Property: Rewrite: Use log 4 7 = 1.404 to evaluate =2(1.404) The value is 2.808

Example 5: Expand log 6 5x 3 - log 6 y log 6 5+ log 6 x 3 - log 6 y log 6 5 + 3log 6 x - log 6 y

Example 6: Expand log 6 4x + log 6 y 2 log 6 4 + log 6 x + log 6 y 2 log 6 4 + log 6 x + 2log 6 y

Example 6: Condense 2log 6 5 + log 6 x - 3log 6 y log 6 5 2 + log 6 x - log 6 y 3 log 6 25 x - log 6 y 3

Example 7: Condense 4ln x – 3ln x ln x 4 – ln x 3 ln x

Change of Base formula This will let us use our calculators!

Example:

1.89

Example:.7737

Example:

p. 510 3-6 all, 8, 12, 16-28 evens, 34-38 evens Graphing Worksheet

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