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Understanding Exponential and Logarithmic Inequalities in Math

Learn how to solve exponential and logarithmic inequalities, explore non-arithmetic and non-geometric sequences and series, and discover how to find terms and formulas using explicit and recursive methods.

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Understanding Exponential and Logarithmic Inequalities in Math

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  1. Math 3 - Module 6 Honors Topics

  2. Exponential and Logarithmic Inequalities • Exponential inequality rules: • Logarithmic inequality rules: If the bases of the exponential inequality are not the same, you must “log both side” to get the variable out of the exponent. **Always check solutions for logarithms- must have only positives after the log

  3. Examples of Exponential and Logarithmic Inequalities • Solve each inequality.

  4. Non-Arithmetic and Non-Geometric Sequences & Series • We studied arithmetic and geometric sequences and series, but there are some sequences and series that are neither arithmetic nor geometric. • Sequences can be generated using any pattern of n, the location and number of each term. • generates the following terms. A table is a good way to organize the terms. *This sequence does not have a common difference or common ratio

  5. Terms of Sequences • Find the first 4 terms of each sequence. Terms: 0, 1/5, 1/3, 3/7 Terms: 5, 7, 11, 19 *These are all explicit formulas, but can you use recursive?

  6. Examples of Recursive Formulas • Find the first 4 terms of each sequence. Terms: -4, -7, -13, -25 Terms: 5, 7, 11, 19 Now that you generated terms, can you write the formulas?

  7. Write Explicit Formulas • You may want to organize the terms in a table to compare the terms to the values of n. • Do you add to n? Subtract? Multiply? Divide? Square it? • Write the explicit formula for the apparent nth term of the sequence. • 1, 4, 7, 10, 13, … Formula: • 2, 5, 10, 17, 26 Formula:

  8. Sigma Notation • Find the indicated sum.

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