Stitz-Zeager_College_Algebra_e-book

This reduces to the linear equation 86 x x 3 which

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Unformatted text preview: (10) + log0.1 x2 Product Rule = log0.1 (10) + 2 log0.1 (x) Power Rule = −1 + 2 log0.1 (x) Since (0.1)−1 = 10 = 2 log0.1 (x) − 1 2 3 3. We have a power, quotient and product occurring in ln ex . Since the exponent 2 applies 3 to the entire quantity inside the logarithm, we begin with the Power Rule with u = ex and w = 2. Next, we see the Quotient Rule is applicable, with u = 3 and w = ex, so we replace 3 3 ln ex with the quantity ln(3) − ln(ex). Since ln ex is being multiplied by 2, the entire quantity ln(3) − ln(ex) is multiplied by 2. Finally, we apply the Product Rule with u = e and w = x, and replace ln(ex) with the quantity ln(e) + ln(x), and simplify, keeping in mind that the natural log is log base e. 3 ex 2 3 ex Power Rule = 2 [ln(3) − ln(ex)] ln Quotient Rule = 2 ln = 2 ln(3) − 2 ln(ex) = 2 ln(3) − 2 [ln(e) + ln(x)] Product Rule = 2 ln(3) − 2 ln(e) − 2 ln(x) = 2 ln(3) − 2 − 2 ln(x) Since e1 = e = −2 ln(x) + 2 ln(3) − 2 4. In Theorem 6.6, there is no mention of how to deal with radicals. However, thinking back to De...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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