High School

Given that [tex]5^5 = 3125[/tex], what is the equivalent exponential equation written in logarithmic form?

A) [tex]5^5 = \log 3125[/tex]
B) [tex]\log 3125 = 5^5[/tex]
C) [tex]\log_5 3125 = 5[/tex]
D) [tex]3125 = \log_5 5^5[/tex]

Answer :

Final answer:

To convert the exponential equation [tex]5^5 = 3125[/tex]to logarithmic form, we use the format log_b(x) = p, resulting in the correct logarithmic form as log(5, 3125) = 5. The correct option is C.

Explanation:

'Given that 55 = 3125, the equivalent exponential equation written in logarithmic form involves converting an exponential equation to its logarithmic form.

The correct format for expressing an exponential equation like bp = x in logarithmic form is logb(x) = p, where b is the base, x is the result, and p is the exponent.

Applying this to the given equation, 55 = 3125, we rewrite it in logarithmic form as log5(3125) = 5. Thus, the correct answer to the question is option C) log(5, 3125) = 5. The correct option is C.