How do you simplify log5(1250)?

1 Answer
Gió
Apr 28, 2016

I found: −log5(2)−3

Explanation:

We can write it as:
log5(1250)=log5(250)−1=−log5(250)=
using the fact that: log(xy)=logx+logy
=−log(2⋅125)=−[log5(2)+log5(125)]=
using the definition of log we get:
=−log5(2)−3

or alternatively we can use the fact that:

log(xy)=log(x)−log(y)
and again:
log(xy)=logx+logy
and write:
log5(1250)=log5(1)−log5(250)=
=log5(1)−log5(2⋅125)=
=log5(1)−[log5(2)+log5(125)]=
using the definition of log again we get:
=0−log5(2)−3=
=−log5(2)−3

Related questions
See all questions in Common Logs
Impact of this question
6377 views around the world
You can reuse this answer
Creative Commons License