Question 1017339
<pre>
We shouldn't use logarithms if we can avoid it.

9<sup>x</sup> = 6561

We recognize 9 as 3<sup>2</sup>

Perhaps 6561 is also a power of 3.  Let's find out:

6561/3 = 2187
2187/3 = 729
729/3 = 243
243/3 = 81
81/3 = 27
27/3 = 9
9/3 = 3
3/3 = 1

Therefore 6561 = 3<sup>8</sup> since it takes
8 divisions by 3 to get to 1.

So 

9<sup>x</sup> = 6561

(3<sup>2</sup>)<sup>x</sup> = 3<sup>8</sup>

3<sup>2x</sup> = 3<sup>8</sup>

Since the bases are the same positive number
that does not equal to 1, we may write the
eponents equal to each other:

2x = 8

 x = 4

Edwin</pre>