Answer :

To solve the equation [tex]\(\log_m 3125 = m\)[/tex], we need to find the value of [tex]\(m\)[/tex] such that when [tex]\(m\)[/tex] is the base of the logarithm, it satisfies the equation.

Here's a step-by-step approach to finding the solution:

1. Understand the Equation: The equation [tex]\(\log_m 3125 = m\)[/tex] means that if 3125 is expressed as a power of [tex]\(m\)[/tex], the exponent is [tex]\(m\)[/tex] itself. In other words, [tex]\(m^m = 3125\)[/tex].

2. Look for Patterns: The best way to solve this is to determine if 3125 can be expressed as a power of any simple number.

3. Exponentiation Check: We suspect a simple base might work, such as a single-digit number. We start by checking small, plausible values of [tex]\(m\)[/tex].

4. Test Small Values:
- Let's test for the base [tex]\(m = 5\)[/tex]:
- Calculate [tex]\(5^5\)[/tex]:
[tex]\[
5^5 = 5 \times 5 \times 5 \times 5 \times 5 = 3125
\][/tex]
- Since [tex]\(5^5 = 3125\)[/tex], we have found that [tex]\(m = 5\)[/tex] satisfies the equation.

5. Conclusion: Therefore, [tex]\(m = 5\)[/tex] is the solution to the equation [tex]\(\log_m 3125 = m\)[/tex].

Thus, the value of [tex]\(m\)[/tex] that satisfies the equation is [tex]\(m = 5\)[/tex].

Thanks for taking the time to read Solve for tex m tex in the equation tex log m 3125 m tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada