Solve Log Question: Find Cube Root of 25 in Base 5

[gabby989062]

Homework Statement

log base 5 cube root 25 equals what?

Homework Equations

I know that the answer is 2/3 because it is in the back of the book

The Attempt at a Solution

log base 5 = 25 to the 1/3

so 5 to the what = 25 to the 1/3

How do I get 5 to the 2/3 equals 25 to the 1/3? This is the only tough question in this section.

 

[hrc969]

Homework Statement

log base 5 cube root 25 equals what?

Homework Equations

I know that the answer is 2/3 because it is in the back of the book

The Attempt at a Solution

log base 5 = 25 to the 1/3

so 5 to the what = 25 to the 1/3

How do I get 5 to the 2/3 equals 25 to the 1/3? This is the only tough question in this section.

write 25 to the 1/3 as 25^(1/3).
but 25=5^2 so 25^(1/3)=(5^2)^(1/3). By your rules about exponents that is equal to 5^(2/3).