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).

 

[Architeuthis Dux]

I would approach this problem by first understanding the concept of logarithms and their relationship to exponents. In this case, we are looking for the base 5 logarithm of the cube root of 25. This can be rewritten as log base 5 (25^(1/3)).

Next, I would use the property of logarithms that states log base b (x^y) = y*log base b (x). Applying this to our problem, we get log base 5 (25^(1/3)) = (1/3)*log base 5 (25).

Now, we know that 25 can be written as 5^2. Substituting this into our equation, we get (1/3)*log base 5 (5^2).

Using another property of logarithms, log base b (b^x) = x, we can simplify this to (1/3)*2 = 2/3. Therefore, the answer to the given problem is 2/3.

It is important to understand the concept behind logarithms and their properties in order to solve problems like this. Simply memorizing the answer may not always be helpful in understanding the underlying concept. I would recommend practicing more problems and seeking help from a teacher or tutor if needed.