Homework Help

What is `log_125 (1/5)` ?                   

user profile pic

kristenmarieb... | Student, Grade 10 | Valedictorian

Posted August 13, 2013 at 5:03 AM via web

dislike 1 like

What is `log_125 (1/5)` ?    


Tagged with algebra2, math

1 Answer | Add Yours

user profile pic

llltkl | College Teacher | Valedictorian

Posted August 13, 2013 at 5:32 AM (Answer #1)

dislike 2 like

Let `log_125(1/5)=x`

Since, `log_ax=n` means that `a^n=x` we can write:


`rArr (5^3)^x=1/5`

`rArr 5^(3x)=1/5`

Taking the log to the base 5 on both sides:


`rArr 3x=-1`

`rArr x=-1/3`

Therefore, `log_125(1/5)=-1/3`

Here, change of base formula can also be applied to get the same result.


Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes