Question

Which of the following is equivalent to log(125) 25?

Answer 1

Answer:3/2

Step-by-step explanation:see if your like me and like getting answers right, its actually 3/2

Answer 2

It is important to note that both 125 and 25 are powers of 5. 5 to the third yields 125, 5 squared yields 25.
By definition of the logarithm, the number we are looking for is the number x for which
`125^x=25` holds. Using the above facts, we get:

`(5^3)^x=5^2 \\ 5^(3x)=5^2`.
Since the bases of the exponents are equal, we can equate the exponents. 3x=2. Hence, x=2/3. This the answer.
`log_(125) (25)= (2)/(3)`