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For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs.$$\ln \left(y \sqrt{\frac{y}{1-y}}\right)$$
$\frac{3}{2} \ln \left(y^{3 / 2}\right)-\frac{1}{2} \ln (1-y)$
Algebra
Chapter 6
Exponential and Logarithmic Functions
Section 5
Logarithmic Properties
Functions
Missouri State University
Campbell University
Harvey Mudd College
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So in this question, were asked to expand this longer, then naturalized. Why times the square root of why? Over one minus y. So we're gonna be rewriting Is a subtraction different? A different Simon Chronicle blocks. So in this case, the first thing we're gonna do is that we know that this could be reinvented. This Helen. Why, plus Ellen Square root of why over one month's mind. Basically, the way that we get this is that if you're multiplying two things by each other down here in the long rhythms, they could be written his addition. So now we know that this on square root here can be taken out. And you could be right. This is Ellen live plus 1/2. How, uh, why were one minus y? And now this is our answer in our simplest form,
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