what's difference between log^3x and logx^3?
2007-01-10 15:53:38 · 7 answers · asked by javalearner 1 in Science & Mathematics ➔ Mathematics
log^3(x) is a fancy way of writting (log(x))^3
Clearly this is different than log(x^3), which can also be
written as 3 * log(x).
2007-01-10 16:00:53 · answer #1 · answered by Andrew 6 · 0⤊ 0⤋
log^3x doesn't mean anything. log x^3 = 3 log x.
If you mean the difference between log (base 3) of x and log (base x) of 3, they will be reciprocals of each other due to the law:
log (base a) of b = log b / log a
If you mean log (3x) vs. log (x^3), the first is equivalent to log 3 + log x and the second is 3 log x as before.
If you mean log (3^x) vs. log (x^3), the first is x log 3 and the second is 3 log x. For instance, if x = 10 (and logs are to base 10) then the first is 10 log 3 ~ 4.8, while the second is 3 log 10 = 3.
If you mean something else, it depends on what you mean!
2007-01-11 00:00:21 · answer #2 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
Suppose you meant log 3^x and log x^3. By definition,
log 3^x = x log 3.
log x^3 = 3 log x.
Edit: If you meant (log x)^3, the answer has been provided.
2007-01-11 00:02:31 · answer #3 · answered by S. B. 6 · 0⤊ 0⤋
log^3 x = (log x)^3
log(x^3) (= 3 log x by a property of logarithms)
The difference is order of operations; in the first one, you take the log then cube. On the second one, you cube first, and then take the log.
2007-01-10 23:58:35 · answer #4 · answered by Professor Maddie 4 · 0⤊ 0⤋
log^3(x) {Which, I've never seen written like that} presumably means [log(x)]^3, the same way sin^2(x) means [sin(x)]^2.
With that being said,
log^3(x) = [log(x)]^3, and
log(x^3) is just what it looks like, log(x^3).
The log property
c * log[base b](a) = log[base b](a^c)
enables us to change log(x^3) into 3logx.
But that's the difference.
log^3(x) = [log(x)]^3 {meaning the log is calculated, and then the result is cubed), whereas
log(x^3) = 3log(x) {meaning you take log(x), and then multiply it by three}.
Two different things.
2007-01-10 23:58:43 · answer #5 · answered by Puggy 7 · 0⤊ 0⤋
log ^ 3 x is ( log x ) ^ 3
log x ^ 3 is 3 times log x.
2007-01-10 23:59:58 · answer #6 · answered by sg 2 · 0⤊ 0⤋
The difference is log^3x doesn't even make sense.
2007-01-10 23:56:54 · answer #7 · answered by math_ninja 3 · 2⤊ 1⤋