Question 1121935
<br>
Given:
{{{log(16,4) = r}}}
{{{log(16,11) = s}}}
{{{log(4,11) = t}}}<br>
To find:
{{{log(16,(4*sqrt(11)))}}}<br>
Using basic logarithm rules,<br>
{{{log(16,(4*sqrt(11))) = log(16,(4))+(1/2)(log(16,11)) = r + (1/2)s}}}<br>
So one form of the answer, according to the given rules, is<br>
r + s/2<br>
There are many other forms for the answer.<br>
Note that t = 2s; so another form of the answer could be<br>
r+t/4<br>
And note further that r is just 1/2; so other forms of the answer are<br>
1/2+t/4<br>
or<br>
1/2+s/2<br>
or<br>
(1+s)/2