Calculus ??? Evaluate Log25 5?

Answer 1

5 is 25 ^ (1/2) so the log(base 25) of 5 = 1/2

Answer 2

Let log be log to base 25 in the following:-
log 5 = x
25^x = 5
x = 1 / 2

Answer 3

log[base 25](5)

One thing we can use is this log property:

log[base a](b) = 1/log[base b](a)

(In essence, we can flip the base and argument if we put one over the log).

With that said,

log[base 25](5) = 1/log[base 5](25)

But 25 = 5^2, so we get

= 1/log[base 5](5^2)

And by another log property, we can move the power of 2 outside of the log.

= 1/( 2log[base 5](5) )

But log[base 5](5) = 1, so

= 1/(2*1)
= 1/2