Homework Help

Rewrite expression using properties of logarithms. `log(x^5/(y^3sqrtz))`

user354582's profile pic

Posted via web

dislike 3 like

Rewrite expression using properties of logarithms.


2 Answers | Add Yours

mjripalda's profile pic

Posted (Answer #1)

dislike 1 like


First, express the radical as exponent.

`= log(x^5/(y^3z^(1/2)))`

Then, apply the quotient property `( log_b(M/N)=log_b M - log_ N)` .



For the second logarithm, apply the product property `( log_b (M*N) = log_bM + log_bN)` .




And, apply the exponent property `(log_bM^a= alog_bM)` .


Hence, `log(x^5/(y^3sqrtz))=5logx-3logy-1/2logz` .

zach2794's profile pic

Posted (Answer #2)

dislike 1 like

First of all you need to know three properties:


log_(a)(B*C)=log_(a)(B)+log_(a)(C) and




Now, convert everything to exponents to make things easier:




Then, separate the fraction inside the logarithm:



Next, separate the multiplication in the second logarithm:



Finally, distribute the negative into the parenthesis and use the last property to move the exponents to the front of the logarithm:



Therefore, log((x^5)/((y^3)(sqrt(z))))=5log(x)-3log(y)-(1/2)log(z)


Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes