Question 381648
{{{log(8, (32))}}}
With expressions like this you want to look to see if<ul><li>the base is an obvious power of the argument, or</li><li>the argument is an obvious power of the base, or</li><li>the base and the argument are both obvious powers of some other number.</li></ul>
It is not obvious what power of 8 32 is. Nor is it obvious what power of 32 8 is. But with a little work we can find that 8 and 32 are both powers of 2. So we can simplify this expression "by hand" if we use the base conversion formula, {{{log(a, (p)) = log(b, (p))/log(b, (a))}}}, to convert the base 8 logarithm into an expression of base 2 logarithms:
{{{log(2, (32))/log(2, (8))}}}
Since {{{32 = 2^5}}} then {{{log(2, (32)) = 5}}}. Similarly, since {{{8 = 2^3}}} then {{{log(2, (8)) = 3}}}. This makes our expression:
5/3