Question 43262
<pre><font size = 5><b>solve for x 
logx 25 = -2 

Use the rule that says: 

A logarithmic equation of the form

  log<sub>B</sub>A = C

is equivalent to and can be rewritten
as the exponential equation

     B<sup>C</sup> = A

So we rewrite

   log<sub>x</sub>25 = -2

as

    x<sup>-2</sup> = 25

Then we write the x<sup>-2</sup> as 1/x<sup>2</sup>

   1/x<sup>2</sup> = 25

Multiply both sides by x<sup>2</sup>:

      1 = 25x<sup>2</sup>

Divide both sides by 25 

   1/25 = x<sup>2</sup> 

Take positive square roots of both sides
(logarithm bases must be positive and <font face = "symbol">¹</font> 1,
by definition)
    
    1/5 = x

Edwin</pre>