SOLUTION: Write each expression in terms of sums, differences, and multiples of logarithms of the variables. a)log base2 x^2 y^4/z^3 w^5 b)ln x^2 multiplied by the cube root of x+4

Question 36198: Write each expression in terms of sums, differences, and multiples of logarithms of the variables.
a)log base2 x^2 y^4/z^3 w^5
b)ln x^2 multiplied by the cube root of x+4
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
USE FORMULAE
LOG(AB)=LOG(A)+LOG(B)
LOG(A/B)=LOG(A)-LOG(B)
LOG(X^N)=N*LOG(X)
Write each expression in terms of sums, differences, and multiples of logarithms of the variables.
a)log base2 x^2 y^4/z^3 w^5=LOG(X^2)+LOG(Y^4)-LOG(Z^3)-LOG(W^5)....ALL TO COMMON BASE 2 AND HENCE IS OMITTED IN TYPING.
=2LOG(X)+4LOG(Y)-3LOG(Z)-5LOG(W).ALL LOGS TO BASE 2
b)ln x^2 multiplied by the cube root of x+4=LN(X^2)+LN{(X+4)^1/3}
=2LN(X)-{LN(X+4)}/3
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