## Fanduekisses one year ago pls help. ;'( use the properties of logarithms to rewrite and simplify the logarithmic expression.

1. Fanduekisses

$\log _{5}(\frac{ 1 }{ 250 })$

2. Fanduekisses

$\log_{5}(1)-\log_{5}(250)$???

3. Fanduekisses

@amistre64 @dan815 @satellite73

4. Fanduekisses

then what?

5. amistre64

the question seems vague. what constitutes a 'simplified' version of it?

6. amistre64

what does log(1) always equal?

7. amistre64

so 250 a multiple of 5 by chance?

8. amistre64

what log properties do you know?

9. Fanduekisses

yes , 50 right

10. Fanduekisses

ohh could I use the change of base ? lol

11. Mertsj

log(base5) of1 = 0 so the simplified version is - log(base5)250

12. Fanduekisses

The answer key says it's -3-log(base 5) (2) but how?

13. amistre64

notifs didnt say nothing about 15 minutes ago ...

14. amistre64

15. Fanduekisses

Power, product, and quotient

16. Mertsj

Or perhaps this: $\log_{5}1-\log_{5}5^3(2)=0-(\log_{5}5^3 +\log_{5}2)=-3-\log_{5}2$

17. Fanduekisses

omg, that makes so much sense, I see what was done there. :D

18. Fanduekisses

Pretty much all the log properties were used there haha. :)