Write log8 3 as a logarithm of base 5.?

1 Answer

• logs are conceptually simple, but

  if you think about them too much, they make you go a little “funny” in the head.

  you know: a little… “funny.”

  they do to me, anyway.

  so

  the thing your nephew needs to do is to learn the few simple rules,

  then practice the heck out of them

  until he doesn’t have to think about them too much.

  as far as your specific question,

  all that’s needed is the “change of base” rule:

  log_b(x) = log_a(x) / log_a(b)

  The very name of the rule gives you confidence, don’t it?

  so

  log_8(3) = log_5(3) / log_5(8)

  there is no way in the rules to simplify into a single log expression.

  any more than that, and I start to go a little… “funny” in the head.

  ♣♦