Given the logarithm expression:

log(n) (1/n^5)

We need to find the value.

First we will rewrite the quotient as a negative power

==> 1/n^5 = n^-5

==> log(n) (1/n^5) = log(n) n^-5

Now we know from logarithm properties that:

log a^b = b*log a

==> log(n) (1/n^5) = log(n) n^-5 = -5*log(n) n

Now we know that log(n) n = 1

==> log(n) 1/n^5 = -5*1 = -5

**Then, the exact values of log(n) (1/n^5) = -5 **

Posted on

We need to find the exact value of log(n)[ 1/n^5], which is logarithm to the base n of 1/n^5.

Now log a^b = b* log a and this applies for logarithm to any base. Also, log (a) a = 1

log(n)[ 1/n^5]

we use 1/ n^5 = n^(-5)

=> log (n) [n^(-5)]

=> -5 * log (n) n

=> -5*1

=> -5

**Therefore log(n)[ 1/n^5] = -5.**

Posted on

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now