Question 766575
<pre>
Learn how to convert a logarithm equation 
into and from an exponential equation. 
That is:

log<sub>B</sub>A = C is equivalent to B<sup>C</sup> = A

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Let x = the answer.  Then

log<sub>16</sub>4 = x, which is equivalent to:

16<sup>x</sup> = 4

Write 16 as (2<sup>4</sup>) and write 4 as 2<sup>2</sup>

(2<sup>4</sup>)<sup>x</sup> = 2<sup>2</sup>

Remove the parentheses by multiplying the exponents:

 2<sup>4x</sup> = 2<sup>2</sup>

When there is one exponential on both sides with the 
same base, and that base is positive and not equal to 1,
then we may set the exponents equal to each other:

 4x = 2
  x = {{{2/4}}}
  x = {{{1/2}}}

Edwin</pre>