Logarithmic and exponential functions - Topics in precalculus

Exponential functions Inverse relations Exponential and logarithmic equations Creating one logarithm from a sum THE LOGARITHMIC FUNCTION WITH BASE b is the function y = logb x. b is normally a number greater than 1 (although it need only be greater than 0 and not equal to 1). Note the following: • For any base, the x-intercept is 1. To see the answer, pass your mouse over the colored area. The logarithm of 1 is 0. y = logb1 = 0. • The graph passes through the point (b, 1). The logarithm of the base is 1. logbb = 1. Proper fractions. • The range of the function is all real numbers. • The negative y-axis is a vertical asymptote (Topic 18). Example 1. And here is the graph of y = ln (x − 2) -- which is its translation 2 units to the right. The x-intercept has moved from 1 to 3. Problem 1. This is a translation 3 units to the left. By definition: logby = x means bx = y. Corresponding to every logarithm function with base b, we see that there is an exponential function with base b: y = bx. Problem 2. and and

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Basic idea and rules for logarithms - Math Insight The basic idea A logarithm is the opposite of a power. In other words, if we take a logarithm of a number, we undo an exponentiation. Exponential and Logarithmic functions Exponential functions Definition Take a > 0 and not equal to 1 . Exponential and Logarithmic functions Exponential functions Definition Take a > 0 and not equal to 1 . Then, the function defined by f : R -> R : x -> ax Logarithms: Introduction to "The Relationship" Purplemath offers a complete lessonon the topic you have selected.Try the lesson below! This lesson is not yet availablein MathHelp.com. Logarithms: Introduction to "The Relationship" (page 1 of 3) Sections: Introduction to logs, Simplifying log expressions, Common and natural logs

Logarithmic Functions The exponential function and the logarithm functions are inverse functions to each other. If we have a logarithm function and if we find the inverse of this, then we have the exponential function. If we draw the graphs of logarithm and exponential function on the line y = x, then we can see that these are the mirror image of each other. For example, for finding the inverse of f(x) = In x, we have to set y = In xInterchanging the role of x and y, we getx = In yex = yf-1(x) = ex Basic Log Rules / Expanding Log Expressions Basic Log Rules / Expanding Logarithmic Expressions (page 1 of 5) Sections: Basic log rules, Expanding, Simplifying, Trick questions, Change-of-Base formula You have learned various rules for manipulating and simplifying expressions with exponents, such as the rule that says that x3 × x5 equals x8 because you can add the exponents. There are similar rules for logarithms. Log Rules: 1) logb(mn) = logb(m) + logb(n)

The Change-of-Base Formula The Change-of-Base Formula (page 5 of 5) Sections: Basic log rules, Expanding, Simplifying, Trick questions, Change-of-Base formula There is one other log "rule", but it's more of a formula than a rule. Working with Exponents and Logarithms What is an Exponent? What is a Logarithm? A Logarithm goes the other way. It asks the question "what exponent produced this?": And answers it like this: