Express log5 in terms of a and b where a=log2 and b=log3
2006-12-10 18:22:18 · 2 answers · asked by gctoinfinity 1 in Science & Mathematics ➔ Mathematics
I'm assuming your "logs" are "common logarithms," that is, logs to base 10.
(I have to make this assumption because (i) no powers of 2 and/or 3 can together give you 5, though with enough powers you might get close to some power of 5; and (ii) the situation is much, much worse for powers of 'e,' the base of "natural logarithms.")
In that case, there is but one obvious way:
5 = 10 / 2, therefore log 5 = 1 - a.
The value of 'b' is redundant; it's simply not needed.
Live long and prosper.
2006-12-10 18:28:57 · answer #1 · answered by Dr Spock 6 · 2⤊ 0⤋
If log refers to the common log, ie in base 10, then
log 5 = log (10/2) = log 10 - log 2 = 1 - a.
2006-12-10 18:29:44 · answer #2 · answered by bictor717 3 · 0⤊ 0⤋