How do you expand #log ((3x(5y))/(3z^2))#?

1 Answer
Dec 21, 2015

Answer:

#log(5)+log(x)+log(y)-2log(z)#

Explanation:

Use the following logarithm rules.

#log(AB) = log(A) + log(B)# Product Rule

#log(A/B) = logA - log(B)# Quotient Rule

#log(A^n) = nlog(A)# Power Rule

Our problem #log((3x(5y))/(3z^2))#
We can cancel out 3 from numerator and denominator.
#log((x(5y))/(z^2))#
Then apply the rules which we saw

#log((x(5y)) - log(z^2)# Applying the Quotient rule.
#log(x)+log(5)+log(y) - log(z^2)# Applying the Product rule.
#log(x)+log(5)+log(y) - 2log(z) # Applying Power Rule.

Re-arranging.
#log(5)+log(x)+log(y)-2log(z)#