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8.3 Logarithmic Functions as Inverses. Def: Logarithm The logarithm to the base b of a positive number y is defined: If y = b x , then log b y = x. Example: Write 729 = 3 6 and (1/2) 3 = 1/8 in log form. 729 = 3 6 can be written as log 3 729 = 6
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Def: Logarithm The logarithm to the base b of a positive number y is defined: If y = bx, then logb y = x
Example: Write 729 = 36 and (1/2)3 = 1/8 in log form. 729 = 36 can be written as log3 729 = 6 and (1/2)3 = 1/8 written as log(1/2) (1/8) = 3
Evaluating Logs Ex. Evaluate log9 27. What number must you raise 9 too, to get 27? So 9x = 27 32x = 33 so 2x = 3 or x = 3/2
Def: A common logarithm is a logarithm that uses base 10. You can write the common log as log10 or just log. log = log10
Graphing log functions. A log function is the inverse of an exponential function. We graph inverses over the line y=x.
The domain of the log is x > 0. The range is all real numbers. The zero is at x = 1. You can only find the log of positive numbers. Logs of numbers less than one are negative and logs of numbers greater than one are positive. We can translate log functions just like any other function we already seen.
