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: In that example: The Exponent takes 2 and 3 and gives 8 (2, used 3 times in a multiplication, makes 8) The Logarithm takes 2 and 8 and gives 3 (2 makes 8 when used 3 times in a multiplication) A Logarithm says how many of one number to multiply to get another number So a logarithm actually gives you the exponent as its answer: (Also see how Exponents, Roots and Logarithms are related.) Working Together Exponents and Logarithms work well together because they "undo" each other (so long as the base "a" is the same): They are "Inverse Functions" Doing one, then the other, gets you back to where you started: Doing ax then loga gives you x back again: Doing loga then ax gives you x back again: It is too bad they are written so differently ... it makes things look strange. going up, then down, returns you back again:down(up(x)) = x (and vice versa) And also:

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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. You may have noticed that your calculator only has keys for figuring the values for the common (base-10) log and the natural (base-e) log, but no other bases.

Understanding and applying the laws of logarithm 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. 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 Logarithms are the "opposite" of exponentials, just as subtraction is the opposite of addition and division is the opposite of multiplication.

It’s the Law Too — the Laws of Logarithms Summary: Do you have trouble remembering the laws of logarithms? Do you know why you can change log(x)+log(y) to a different form, but not log(x+y)? This page helps you make sense out of the laws of logarithms. See also: All the laws of logarithms flow directly out of the laws of exponents. If you feel a bit unsteady with the laws of exponents, please review them before going on. 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 The graph of function is given below

CHANGING THE BASE OF A LOGARITHM Let a, b, and x be positive real numbers such that and (remember x must be greater than 0). Then Exponential and Logarithmic functions Exponential functions Definition Take a > 0 and not equal to 1 . Then, the function defined by 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 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.

Related: MA304 Exponential and Logarithmic Functions • MA304 Exponential and Logarithmic Functions