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Log question

1. Homework Statement

log base 5 cube root 25 equals what?


2. Homework Equations

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

3. 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. :cry:
1. Homework Statement



2. Homework Equations



3. The Attempt at a Solution
 

Answers and Replies

68
0
1. Homework Statement

log base 5 cube root 25 equals what?


2. Homework Equations

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

3. 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. :cry:
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).
 

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