if log a= x and log b = y,
then what is 1/3 log (ab)^3？
well first of all:
1/3 log (ab)^3
= (1/3)(3) log (ab) = log (ab)
now log (ab) = log a + log b
(that is how your slide rule works)
(you do not have a slide rule?)
(google slide rule :)
so what we have here is
x+y
http://en.wikipedia.org/wiki/Slide_rule
Now about that power stuff,
If we can agree that
log(ab) = log (a) + log (b)
then what is log (a^3) ????
well
log (a*a*a) = log(a)+log(a)+log(a)
which is of course
3 log (a)
:)
To find the value of 1/3 log((ab)^3), we can start by simplifying the expression.
First, let's rewrite the expression using the properties of logarithms:
1/3 log((ab)^3) = log((ab)^3)^(1/3)
Applying the power rule of logarithms, we can rewrite the expression as:
log(a^3b^3)^(1/3)
Since log(a^b) = b * log(a), we can further simplify the expression:
(1/3) * 3 * (log(a) + log(b))
Now, substituting the given log values:
(1/3) * 3 * (x + y)
Simplifying further:
x + y
Therefore, the value of 1/3 log((ab)^3) is equal to x + y.