Question

If r=cube root of A^2B/C then log r can be represented by

Answer 1

First, I will write the expression clearly:


`r= \sqrt[3]{ (A^(2)B)/C }`


`r= (A^(2)B/C)^(1/3)`

Next, use these logarithm properties

log (x^n) = nlog(x)

log(xy/z) = log x + log y - log z

Then,

log r = log {(A^2)B/C}^(1/3) = (1/3) [ 2logA + logB - log C]