Logarithms and Exponents What do I do Describe
Logarithms and Exponents
What do I do? Describe the function. x f(x) = 2 This function raises 2 to the x power.
What would my inverse do? Recall that two functions are inverse functions if the input (domain) of the first function becomes the output (range)of the second function and the output (range) of the first function becomes the input (domain) of the second function. What is the domain of the original function? The x or the exponent What is the range of the original function? The value of 2 raised to the power
What would my inverse do? The inverse would take 2 raised to a power (range of the original now domain of the inverse) and determine the exponent that gives you the answer (domain of the original function now range of the inverse) How would you write this function?
Logarithmic Function log·a·rithm The power to which a base, such as 10, must be raised to produce a given number. If nx = a the logarithm of a, with n as the base, is x; symbolically, logn a = x. For example, 103 = 1, 000; therefore, log 10 1, 000 = 3.
Exponential Function 3 2 = 8 Base exponent argument Logarithmic Function log 2 8= 3 Base argument exponent
Practice evaluating Logarithms Complete the problems In section V on the worksheet. Write the problems in words before solving Example: log 8 64 What exponent do you raise 8 to in order to get an answer of 64? Answer = 2
Practice converting Exponential to Logarithmic Work problems in section VI on the worksheet. Convert the exponential function to a logarithmic function.
Solving Logarithmic Equations log 2 x = 4 Simply think about what this problem says. The base (2) is raised to the exponent answer (4) to get the argument x. 24 = x x = 16
Solving Logarithmic Equations Work problems in section VII on the worksheet. Write the problems in words before solving. Example: log 3 x = 2 The base 3 is raised to the exponent (answer) 2 to get the argument x. 32 = x or 32=9 Understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents. [F-BF 5]
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