Question 1109806
<pre>
The three main rules of logs to use on theses are:

1.   A&#8729;log(B) = log(B<sup>A</sup>)
2.   log(A)+log(B) = log(A&#8729;B)
3.   log(A)-log(B) = log(A/B}

I'll do 2) and 3).  You do the others:

2)  2log(12)-(1/2)log(9)-3log(2)

    log(12<sup>2</sup>)-log(9<sup>1/2</sup>)-log(2<sup>3</sup>)
    log(144)-log(3)-log(8)
    log(144/3)-log(8)
    log(48)-log(8)
    log(48/8)
    log(6)  


3)  3log(x)-2log(y)+5log(z)
    log(x<sup>3</sup>)-log(y<sup>2</sup>)+log(z<sup>5</sup>)
    log(x<sup>3</sup>/y<sup>2</sup>)+log(z<sup>5</sup>)
    log[(x<sup>3</sup>/y<sup>2</sup>)&#8729;(z<sup>5</sup>)]
    log(x<sup>3</sup>z<sup>5</sup>/y<sup>2</sup>)

Edwin</pre>