Question 604023
When I looked at this problem, I found a solution by recognizing...<ul><li>Since {{{32 = 2^5}}} it will be possible to express log(32) in terms of log(2):
{{{log((32)) = log((2^5)) = 5*log((2))}}}
using the property {{{log(a, (p^q)) = q*log(a, (p))}}}</li><li>The property {{{log(a, (p/q)) = log(a, (p)) - log(a, (q))}}} can be used to separate the 2 and the 5:
{{{log((2/5)) = a}}}
{{{log((2)) - log((5)) = a}}}
From this we can get an expression for log(2):
{{{log((2)) = a + log((5))}}}</li></ul>
Substituting this expression into the log(32) expression we get:
{{{log((32)) = log((2^5)) = 5*(a + log((5)))}}}
Distributing the 5 we get:
{{{log((32)) = log((2^5)) = 5*(a + log((5))) = 5a + 5log((5))}}}
which expresses log(32) in terms of a.