Question 670883
i believe you are looking for the natural log of root4(9r^8s)
root4 is equivalent to taking the fourth root of which is equivalent to raising to the 1/4 power, so we get:
ln ((9r^8s)^(1/4))
this becomes:
(1/4) * ln ((9r^8s) which becomes:
(1/4) * [ ln(9) + ln(r^8s) ] which becomes:
(1/4) * ln(9) + (1/4) * ln(r^8s) which becomes:
(1/4) * ln(9) + (1/4) * 8 * s * ln(r)
to confirm this was done correctly, i let r = 2 and s = 3 and i solved using both the original expression and the final expression and got the same answer of 4.70819 rounded to 5 decimal places.
the concepts you use are:
log(a^b) = b*log(a)
log((a^b)^c) = c*log(a^b) = b*c*log(a)
log(a*b) = log(a) + log(b)