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

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on


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

zach2794 | Student, Undergraduate | (Level 1) eNoter

Posted on

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)


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