SOLUTION: express as a sums/difference log17 (x^3y^5/z^4) I goofed on the previous question posted.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: express as a sums/difference log17 (x^3y^5/z^4) I goofed on the previous question posted.       Log On


   

Question 288337: express as a sums/difference log17 (x^3y^5/z^4) I goofed on the previous question posted.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The reference to "sums/differences" should bring to mind two of the properties of logarithms:
  • <log%28a%2C+%28p%2Aq%29%29+=+log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29
  • <log%28a%2C+%28p%2Fq%29%29+=+log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29

log%2817%2C+%28x%5E3y%5E5%2Fz%5E4%29%29
We can start by using the second property, because of the division:
log%2817%2C+%28x%5E3y%5E5%29%29+-+log%2817%2C+%28z%5E4%29%29
And now the first property because of the multiplication:
log%2817%2C+%28x%5E3%29%29+%2B+log%2817%2C+%28y%5E5%29%29+-+log%2817%2C+%28z%5E4%29%29
This may the the desired answer. Or you could use a third property, log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29, to move the exponents out in front:
3log%2817%2C+%28x%29%29+%2B+5log%2817%2C+%28y%29%29+-+4log%2817%2C+%28z%29%29