 # 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. Logs "undo" exponentials. In practical terms, I have found it useful to think of logs in terms of The Relationship: On the left-hand side above is the exponential statement "y = bx". If you can remember this relationship (that whatever had been the argument of the log becomes the "equals" and whatever had been the "equals" becomes the exponent in the exponential, and vice versa), then you shouldn't have too much trouble with logarithms. (I coined the term "The Relationship" myself. Convert "63 = 216" to the equivalent logarithmic expression.

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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?": Logarithmic and exponential functions - Topics in precalculus Exponential functions Inverse relations Exponential and logarithmic equations Proofs of Logarithm Properties (with worked solutions & videos) OML Search In these lessons, we will look at the four properties of logarithms and their proofs. They are the product rule, quotient rule, power rule and change of base rule. You may also want to look at the lesson on how to use the logarithm properties. Logarithmic and exponential functions - Topics in precalculus Exponential functions Inverse relations Exponential and logarithmic equations Creating one logarithm from a sum

from Wolfram MathWorld The natural logarithm is the logarithm having base e, where This function can be defined 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 can be converted to the base b by the formula Let's verify this with a few examples. Exponential Function Reference This is the Exponential Function: f(x) = ax a is any value greater than 0 Properties depend on value of "a" When a=1, the graph is a horizontal line at y=1 Apart from that there are two cases to look at: a between 0 and 1 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. Let's start with simple example. If we take the base and raise it to the power of , we have the expression . The result is some number, we'll call it , defined by .

Logarithmic Functions The section covers: Half-Life problems can be found here. What is a Log and Why do we Need Them? I have to admit that logs are one of my favorite topics in math. I’m not sure exactly why, but you can do so many awesome things with them! 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:

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