Question 108483
dont know how to do this problem because of the square root, I couldnt even write it correctly on this post. Help!
Given that {{{ log ( 2, 5 ) = 2.3219}}} and {{{ log ( 2, 7 ) = 2.8074}}} , evaluate {{{ log ( 2, sqrt(35)) }}} 
<pre><b>
First we change the square root to the {{{1/2}}} power,
since they are equivalent:

So the first step is to change 

{{{ log ( 2, sqrt(35)) }}}

to

{{{ log ( 2, 35^(1/2))) }}}

Second step is to move the exponent {{{1/2}}}
in front of the logarithm as a coefficient:

{{{1/2}}}{{{log ( 2, 35)) }}} 

Third step is to write {{{35}}} as {{{5*7}}} 
So we now have

{{{1/2}}}{{{log ( 2, 5*7)) }}}

Fourth step, we put parentheses around the logarithm

{{{1/2}}}{{{(log ( 2, 5*7))) }}}

Fifth step, we write the {{{log(2,5*7)}}} as {{{log(2,5)+log(2,7)}}}
so now we have

{{{1/2}}}{{{(log(2,5)+log(2,7))}}}

Sixth step, we substitute the given decimal values for the logarithms,
that is, {{{ log ( 2, 5 ) = 2.3219}}} and {{{ log ( 2, 7 ) = 2.8074}}}
so we now have

{{{1/2}}}{{{(2.3219+2.8074)}}}

Seventh step, we evaluate the whole thing with a calculator:

Answer: {{{2.56465}}}

Edwin</pre>