As we know from [i]Special functions[/i] -section, logarithmic functions are inverse of exponential functions. Thus[br][br]   [math]\Large \textcolor{blue}{y=a^x\;\;\Leftrightarrow\;\;x=\log_a(y)}[/math].[br][br]Logarithmic functions are defined only with positive real numbers ([math] \cal R^+[/math]) but the solution can be any real number ([math] \cal R[/math]). All logarithmic functions go through the point (1, 0). From the definition, we can easily see some basic properties of logarithmic:[br][br]   [math]\large\begin{eqnarray}[br]a^1=a &\Leftrightarrow&\log_a(a)=1\\[br]a^0=1 &\Leftrightarrow&\log_a(1)=0[br]\end{eqnarray}[/math][br][br]Logarithms are sometimes thought to be difficult concept. In fact, they are very easy, if you read them correctly. For example, [math]\textcolor{blue}{\log_a(x)}[/math] is read: [color=#0000ff]to which power should the [i]a[/i] be raised to get [i]x[/i][/color].[br][br]Commonly used symbol for logarithmic of base [i]e[/i] is [color=#0000ff]ln[/color] and for logarithmic of base 10 is [color=#0000ff]lg[/color] . These symbols are used during the lessons. Check your own calculator, how they are denoted there. There are also differences among mathematical programs, so check the correct syntax from a manual.[br][br][br]

  [math]\large\begin{eqnarray}[br]\log_2 8=3&\text{as}&2^3=8\\[br]\lg 100=2&\text{as}&10^2=100[br]\end{eqnarray}[/math][br]

[br][math]\large[br]\log_4 (x-2)=3 \Leftrightarrow x-2=4^3 \Leftrightarrow x=64+2=66[br][/math][br][br][math]\large[br]\log_x (81)=2 \Leftrightarrow x^2=81\Leftrightarrow x=9[br][/math][br]