Question

log 3125 Best root 5

Answer 1

Evaluate log base 5 of square root of 3125

log5(√3125)log5(3125)

Rewrite 31253125 as 252⋅5252⋅5.



Factor 625625 out of 31253125.

log5(√625(5))log5(625(5))

Rewrite 625625 as 252252.

log5(√252⋅5)log5(252⋅5)

Pull terms out from under the radical.

log5(25√5)log5(255)

Rewrite log5(25√5)log5(255) using the change of base formula.

The change of base rule can be used if aa and bb are greater than 00 and not equal to 11, and xx is greater than 00.

log a(x)=log b(x)log b(a)log a(x)=log b(x)log b(a)

Substitute in values for the variables in the change of base formula, using b=10b=10.

log(25√5)log(5)log(255)log(5)

The result can be shown in both exact and decimal forms.

Exact Form:

log(25√5)log(5)log(255)log(5)

Decimal Form:

2.5