  # log equation

<p>My book has these steps for evaluating a logarithmic equation and I don't quite understand what is going on. It says...
log (2) x(x-4)=5
x(x-4)=2^5 <---------> this is the level I am getting problems... how does log(2) divide the 5 on the other side and end up getting 2^5 ??
By the way this is how the equation continues( which I understand)
X^2-4x -32
(x-8)(x+4)= 0
x=8 x=-4</p>

<p>You may want to look up the definition of logs. They aren't the usual operators, such as multiply and divide, so you can't simply "divide" both sides by log 2. </p>

<p>In fact, logarithms are essentially a shortcut of exponents. It expresses them in a different format, allowing for an altered look and possibly easier manipulation.</p>

<p>Essentially, the logarithm definition goes like this:</p>

<p>Log (a) b = x is the same as a^x = b. That's just a simple rule that you have to memorize. Knowing that, you can probably figure out the first step of this problem pretty easily, by simply applying the definition of a logarithm.</p>

<p>You don't divide, you took the inverse of log (which I know the name implies dividing, but it is not, it's just like how we use arcsin(x) for sin(x)). The base is 2, not your regular 10.</p>