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Rewrite expression using properties of logarithms. `log(x^5/(y^3sqrtz))`
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High School Teacher
First, express the radical as exponent.
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` .
Posted by mjripalda on June 18, 2013 at 5:09 AM (Answer #1)
First of all you need to know three properties:
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:
Posted by zach2794 on June 18, 2013 at 5:53 AM (Answer #2)
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