SOLUTION: 10log(x)-7 log(y)+5 log(z) I keep getting: {{{log(((x^10)/(y^7z^5)))}}} But this is wrong, why?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 10log(x)-7 log(y)+5 log(z) I keep getting: {{{log(((x^10)/(y^7z^5)))}}} But this is wrong, why?      Log On


   

Question 311997: 10log(x)-7 log(y)+5 log(z)
I keep getting: log%28%28%28x%5E10%29%2F%28y%5E7z%5E5%29%29%29
But this is wrong, why?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

What you got is what the answer would have been if
the sign of the third term had been " - " and not " + ". 

Here's the right way. Pay close attention to the signs
and the log rules:

10log%28%28x%29%29-7log%28%28y%29%29%2B5log%28%28z%29%29

Use the rule A%2Alog%28%28C%29%29=log%28%28C%5EA%29%29 on all three terms,
to change the coefficients to exponents:

log%28%28x%5E10%29%29-log%28%28y%5E7%29%29%2Blog%28%28z%5E5%29%29

Use the rule log%28%28A%29%29-log%28%28C%29%29=log%28%28A%2FC%29%29

to write the first two terms as the log of a quotient:

log%28%28%28x%5E10%29%2F%28y%5E7%29%29%29%2Blog%28%28z%5E5%29%29

Use the rule log%28%28A%29%29%2Blog%28%28C%29%29=log%28%28AC%29%29

to write those two terms as the log of a product:

log%28%28%28%28x%5E10%29%2F%28y%5E7%29%29%28z%5E5%29%29%29

Put the second factor in the parentheses over 1:

log%28%28%28%28x%5E10%29%2F%28y%5E7%29%29%28z%5E5%2F1%29%29%29

Multiply the two tope and the two bottoms:

log%28%28%28x%5E10z%5E5%29%2F%28y%5E7%29%29%29

Edwin