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

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Jan 25, 2024 47 likes •153 views

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

SLIDE 1

Definition of a Logarithm

y = logb x if and only if x = by (1)

Alan H. SteinUniversity of Connecticut

SLIDE 2

Definition of a Logarithm

y = logb x if and only if x = by (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

SLIDE 3

Definition of a Logarithm

y = logb x if and only if x = by (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 blogb x = x

Alan H. SteinUniversity of Connecticut

SLIDE 4

Definition of a Logarithm

y = logb x if and only if x = by (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 blogb x = x and logb bx = x. (2)

Alan H. SteinUniversity of Connecticut

SLIDE 5

Properties of Logarithms

Each of the properties of exponential functions has an analog for logarithmic functions.

Alan H. SteinUniversity of Connecticut

SLIDE 6

Properties of Logarithms

Each of the properties of exponential functions has an analog for logarithmic functions.

◮ logb(xy) = logb x + logb y

Alan H. SteinUniversity of Connecticut

SLIDE 7

Properties of Logarithms

Each of the properties of exponential functions has an analog for logarithmic functions.

◮ logb(xy) = logb x + logb y ◮ logb(x/y) = logb x − logb y

Alan H. SteinUniversity of Connecticut

SLIDE 8

Properties of Logarithms

Each of the properties of exponential functions has an analog for logarithmic functions.

◮ logb(xy) = logb x + logb y ◮ logb(x/y) = logb x − logb y ◮ logb(xr) = r logb x

Alan H. SteinUniversity of Connecticut

SLIDE 9

Properties of Logarithms

SLIDE 10

Properties of Logarithms

Each of the properties of exponential functions has an analog for logarithmic functions.

◮ logb(xy) = logb x + logb y ◮ logb(x/y) = logb x − logb y ◮ logb(xr) = r logb x ◮ logb 1 = 0.

In other words, The logarithm of a product or quotient is the sum

r 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