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Logarithms – definition and basic expressions (part 1) – pg.2/10

Posted in Math Theory by Lia on 04/08/2013

pg. 1, 2, 345678910

 

2. Logarithms’ definition and basic expressions (part 1)

 

Logarithmic expressions are the inverse of exponential expressions.

Logarithmic expression of a number is the exponent power to which the base is raised to get that number.

 

Let’s start with the basic exponential expression:

 

[1]

{}{m^n=p}{}

written as a logarithmic expression, expression [1]  becomes:

 

[2]

{log_m}p = n

where “m” is the logarithm’s base.

 

Note:

The conditions for which an exponential expression, [1], can be written as a logarithmic expression, are:

1. {{}{m >0}{}}” title=”{{}{m >0}{}}”/><img src=

2. {m<>1}” title=”{m<>1}”/><img src= (for {m = 1}, {{}{n}{}} is undefined)

3. {p<>0}” title=”{p<>0}”/><img src= (for {p = 0}, {{}{n}{}} is undefined)

 

Examples:

* the exponential expression 64= {2^6} written as a logarithmic expression is {log_2}64 = 6

* the exponential expression 125= {5^3} written as a logarithmic expression is {log_5}125 = 3

When  n = 1  {}{right}{}   p = m  and when  n = 0  {}{right}{}  p = 1  or we can write:

  {{m^1} = m}

  {}{right}{}

  {{log_m}m = 1}

{}{}{}{}{}{{m^0} = 1}{}{}{}{}{}

{}{}{}{}{}{right}{}{}{}{}{}

{}{}{}{}{}{{log_m}1 = 0}{}{}{}{}{}

 

pg. 1, 2, 345678910

 

 

 

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