Question

Evaluate the logarithm log 17 square root 17 (Picture provided)

Answer 1

The answer is 1/2 ⇒ answer (a)

Explanation:

*The logarithm function is the inverse of the exponential function

- Ex: If 2³ = 8 ⇒ then
`log_(2)(8) = 3`

Vice versa : If
`log_(5)(125)=3` ⇒ 5³ = 125

* In logarithm function:

- If
`log_(a)a=1` because
`a^(1)=a`

- If
`log_(a)a^(n)=(n)log_(a)a=n`

∵
`log_(17)√(17)=log_(17)(17)^{(1)/(2)}`

- √b =
`b^{(1)/(2)}`

∴
`log_(17)(17)^{(1)/(2)}=(1)/(2)log _(17)(17)=(1)/(2)(1) = (1)/(2)`

∴ The answer is 1/2 ⇒ answer (a)

Answer 2

Answer: option a.

Explanation:

By definition we know that:

`log_a(a^n)=n`

Where a is the base of the logarithm.

We also know that:

`√(x)=x^{(1)/(2)}`

Then you can rewrite the logarithm given in the problem, as you can see below:

`log_(17)(√(17))`

And keeping on mind the property, you obtain:

`=log_(17)(17^{(1)/(2)})=(1)/(2)`

Therefore, you can conclude that the answer is the option a.