SOLUTION: Use law of logarithms to evaluate: log5 (1000/8)= ? *log(1000/8)to the base of 5.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Use law of logarithms to evaluate: log5 (1000/8)= ? *log(1000/8)to the base of 5.      Log On


   

Question 374255: Use law of logarithms to evaluate:
log5 (1000/8)= ?
*log(1000/8)to the base of 5.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure what "law of logarithms" is so thsi may not be what you are looking for.

log%285%2C+%281000%2F8%29%29
First we'll simplify the argument. 1000/8 = 125:
log%285%2C+%28125%29%29
125+=+5%5E3 so this becomes:
log%285%2C+%285%5E3%29%29
If you understand what this logarithm stands for then you know that this simplifies to 3. If not, then we can use a property of logarithms, log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29, to move the exponent of the argument out in front:
3%2Alog%285%2C+%285%29%29
Since log%285%2C+%285%29%29+=+1 by definition, this becomes:
3*1
or
3