Definition of a Logarithm y = log b x if and only if x = b y (1) - PowerPoint PPT Presentation

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Definition of a Logarithm y = log b x if and only if x = b y (1) Alan H. SteinUniversity of Connecticut Definition of a Logarithm y = log b x if and only if x = b y (1) Essentially, the logarithm to the base b of a number x is the power which

Definition of a Logarithm y = log b x if and only if x = b y (1) Alan H. SteinUniversity of Connecticut
Definition of a Logarithm y = log b x if and only if x = b y (1) Essentially, the logarithm to the base b of a number x is the power which b must be raised to in order to obtain x. Alan H. SteinUniversity of Connecticut
Definition of a Logarithm y = log b x if and only if x = b y (1) Essentially, the logarithm to the base b of a number x is the power which b must be raised to in order to obtain x. This immediately leads to the two very useful formulas b log b x = x Alan H. SteinUniversity of Connecticut
Definition of a Logarithm y = log b x if and only if x = b y (1) Essentially, the logarithm to the base b of a number x is the power which b must be raised to in order to obtain x. This immediately leads to the two very useful formulas b log b x = x and log b b x = x . (2) Alan H. SteinUniversity of Connecticut
Properties of Logarithms Each of the properties of exponential functions has an analog for logarithmic functions. Alan H. SteinUniversity of Connecticut
Properties of Logarithms Each of the properties of exponential functions has an analog for logarithmic functions. ◮ log b ( xy ) = log b x + log b y Alan H. SteinUniversity of Connecticut
Properties of Logarithms Each of the properties of exponential functions has an analog for logarithmic functions. ◮ log b ( xy ) = log b x + log b y ◮ log b ( x / y ) = log b x − log b y Alan H. SteinUniversity of Connecticut
Properties of Logarithms Each of the properties of exponential functions has an analog for logarithmic functions. ◮ log b ( xy ) = log b x + log b y ◮ log b ( x / y ) = log b x − log b y ◮ log b ( x r ) = r log b x Alan H. SteinUniversity of Connecticut
Properties of Logarithms
Properties of Logarithms Each of the properties of exponential functions has an analog for logarithmic functions. ◮ log b ( xy ) = log b x + log b y ◮ log b ( x / y ) = log b x − log b y ◮ log b ( x r ) = r log b x ◮ log b 1 = 0. In other words, The logarithm of a product or quotient is the sum or difference of logarithms and the logarithm of a number to a power is the power times the logarithm of that number. Alan H. SteinUniversity of Connecticut

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