SOLUTION: Use the Laws of Logarithms to expand the expression.
ln sqrt 9r^8s.... instead of a regular sqrt its a cubed root but its not a 3 its 4.Its the sqrrot sigh with a little 4
Algebra ->
Functions
-> SOLUTION: Use the Laws of Logarithms to expand the expression.
ln sqrt 9r^8s.... instead of a regular sqrt its a cubed root but its not a 3 its 4.Its the sqrrot sigh with a little 4
Log On
Question 670883: Use the Laws of Logarithms to expand the expression.
ln sqrt 9r^8s.... instead of a regular sqrt its a cubed root but its not a 3 its 4.Its the sqrrot sigh with a little 4 Found 2 solutions by stanbon, Theo:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! ln sqrt 9r^8s.... instead of a regular sqrt its a cubed root but its not a 3 its 4.Its the sqrrot sigh with a little 4
---------------------------
ln [4th root of 9r^8s] = ln[r^2*4th root of(9s)]
----
= ln(r^2) + ln(4th root of (9s)]
--
= 2ln(r) + (1/4)ln(9s)
---------------------------
cheers,
Stan H.
You can put this solution on YOUR website! 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)
(