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Easy Steps ToUnderstand Logs

1Know the difference between logarithmic andexponentialequations.This is a verysimple first step. If it contains a logarithm (for example: logax = y)it is logarithmicproblem. A logarithm is denoted by the letters "log". If the equation contains anexponent (that is, a variable raised to a power) it is an exponential equation. An

exponent is a superscript number placed after a number. Logarithmic: logax = y Exponential: ay= x

2Know the parts of a logarithm.The base is the subscript number found after the

letters "log"--2 in this example. The argument ornumberis the number following the

subscript number--8 in this example. Lastly, the answer is the number that thelogarithmic expression is set equal to--3 in this equation.

3Know the difference between a common log and a natural log.

Common logshave a base of 10. (for example, log10x). If a log is written without a base(as log x), then it is assumed to have a base of 10.

Natural logs: These are logs with a base of e.eis a mathematical constant that isequal to the limit of (1 + 1/n)nas n approaches infinity, approximately 2.718281828. (It

has many more digits than those written here.) logex is often written as ln x.

Other Logs: Other logs have the base other than that of the common log andthe Emathematical base constant. Binarylogs have a base of 2 (for the example,

log2x).Hexadecimallogs have the base of 16 (for the example log16x (or log#0fx in the

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notation of hexadecimal). Logs that have the 64thbase are indeed quite complex, and

therefore are usually restricted to the Advanced Computer Geometry (ACG) domain.

4Know and apply the properties of logarithms.The properties of logarithms allow youto solve logarithmic and exponential equations that would be otherwise impossible.These only work if the base aand the argument are positive. Also the base acannot be1 or 0. The properties of logarithms are listed below with a separate example for eachone with numbers instead of variables. These properties are for use when solvingequations.

loga(xy) = logax + logayA log of two numbers, xand y, that are being multiplied by each other can be split into

two separate logs: a log of each of the factors being added together. (This also works inreverse.)

Example:

log216 =

log28*2 =

log28 + log22

5Practice using the properties.These properties are best memorized by repeated use

when solving equations. Here's an example of an equation that is best solved with one

of the properties:

4x*log2 = log8 Divide both sides by log2.

4x = (log8/log2) Use Change of Base.

4x = log28 Compute the value of the log.

4x = 3Divideboth sides by 4.

x = 3/4 Solved.

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