Question

Evaluate the logarithm log525

Question 6 options:

1

5

-2

2

Answer 1

`log_(5)(25)` =1.

Explanation:

Given :
`log_(5)(25)`.

To find : Evaluate the logarithm.

Solution : We have given
`log_(5)(25)`.

We can write the 25 as
`5^(2)`.

Then
`log_(5)(5^(2))`.

By the logarithm rule :

(i)
`log_(x)(x^(n))` =
`nlog_(x)(x)`.

(ii)
`log_(x)(x)` = 1.

Here x = 5 , n= 2.

`log_(5)(5^(2))` =
`2log_(5)(5)`.

`2log_(5)(5)`

`log_(5)(5)` = 1.

2* 1 = 2.

Therefore,
`log_(5)(25)` =1.

Answer 2

I think the question is to evaluate the logarithm of 25 on basis 2.

This is:


`log_5 25=log_5(5^2)=2log_55=2(1)=2`

I used these propertites:


`1)log_b(a^n)=nlog_ba 2)log_aa=1`

Answer: 2