What is logˇ5 25√5?

Question

The ˇ5 in my equation means that the base is 5. I was thinking that the answer is ;

logˇ5 25√5
logˇ5 25 (Square root of 5 which is 2.236067978)
logˇ5 55.9016994
= 2.5

Does anyone else have any other ideas?

Answer 1

5/2

5^x = 25√5
5^x = 5² * 5^(1/2)
Add exponents since there is a common base.
5^x = 5^(2 + 1/2)
5^x = 5^(5/2)

x = 5/2

Answer 2

you can solve by follow the rules of log without using the calculator.

log base5 25√5
= log base 5 (5^2)(5^(1/2))
= log base 5 (5^(2 + 1/2))
= log base 5 (5^5/2)
= 5/2 log base 5 5
= 5/2 (1)
= 5/2
= 2.5

Answer 3

25*root(5)=(5^2)*5^(1/2)
=5^(5/2)
so log base(5) of 25 root(5)=5/2

Answer 4

Simplest way:
25√5 = 5²*5^(1/2) = 5^(2.5)
So log_5 5^(2.5) = 2.5
since log _5 5^x = x for any x.