Question 1083245
What is the least integer greater than log<sub>3</sub>38?
<pre>
I think this is the way your teacher expects you to find the
answer:

log<sub>3</sub>38 means 

<I><b><font size=5>the exponent to which 3 must be raised to give 38.</i><b></font>
So to find the least integer greater than that exponent, 
we begin by trying integer exponents of 3 until we find 
the smallest integer such that when 3 is raised to that 
power, the answer is greater that 38.  

We begin by trying exponent 1:

3<sup>1</sup> = 3  <--smaller than 38, so we try the next integer 2.

3<sup>2</sup> = 3×3 = 9  <--still smaller than 38, so we try 3

3<sup>3</sup> = 3×3×3 = 27  <--still smaller than 38, so we try 4

3<sup>4</sup> = 3×3×3×3 = 81  <--that's it!  for 81 is greater than 38

So the least integer greater than log<sub>3</sub>38 is 4.

Edwin</pre>