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Condense logarithms practice11/12/2022 Practice Condense into a single logarithm using the properties of logarithms 1. Practice Expand using the properties of exponents 1. Laws/Properties of Exponents Review ( a is a nonzero real number) leave the same base, add exponents leave the same base, subtract exponents leave the same base, multiply exponents raise each base to the exponent outside parentheses flip the base and make the exponent positive (find the reciprocal) any base to the zero power = 1 Practice Conversions Rewrite the expression in exponential form Rewrite the expression in logarithmic form Special Bases Common logarithms = base 10 Natural logarithms = base e Write the expression as a single logarithm whose coefficient is 1. Use properties of logarithms to condense each logarithmic expression. You can also add, subtraction, multiply, and divide and complete any arithmetic you need. Intermediate Algebra for College Students a. The Math Calculator will evaluate your problem down to a final solution. Logarithms To calculate a logarithm, you should convert it to exponential form **logarithm = the exponent on the base Logarithmic form Exponential form Base Exponent Step 1: Enter the expression you want to evaluate. Graph Transformations Describe how the graph changes from y=ln x : 1. Graphs of Logarithmic Functions Make a table of values, then use transformations to shift the graph Vertical asymptote x =0 Domain: x > 0 Range: All real numbers 1 b 0 1 -1 1/b y x Logarithmic Functions The inverse of an exponential function Exponential Logarithmic function function 2 1 1 0 1/2 -1 y x 1 2 0 1 -1 1/2 y x CONDENSE LOGARITHMS PRACTICE HOW TOOne-to-one functions Functions which have 1-to-1 correspondence: every x and y pair are unique every x has one corresponding y every y has one corresponding x no x repeats & no y repeats How to determine if functions are 1-to-1: Does every element of the domain ( x ) correspond to one and only one member in the range ( y )? Įxamples & Non-examples 1-to-1 Functions Not 1-to-1 Functions 5. Logarithms One-to-One Functions Definition Evaluate Properties
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