Math Problem Statement

Find the value of log base 5 of 125.

Solution

The image contains a math problem involving the fraction 1125\frac{1}{125} and an expression written as "log5." This seems to refer to a logarithmic question.

The problem is asking for the value of the logarithm of 125 to the base 5. Mathematically, it is expressed as:

log5(125)\log_5(125)

To solve this, we need to recognize that 125 can be written as a power of 5. Since 125=53125 = 5^3, we have:

log5(125)=log5(53)\log_5(125) = \log_5(5^3)

Using the logarithmic rule logb(bx)=x\log_b(b^x) = x, the equation simplifies to:

log5(53)=3\log_5(5^3) = 3

Thus, log5(125)=3\log_5(125) = 3.

Would you like further details on this process or any other questions related to logarithms? Here are some related topics you might find interesting:

  1. How to convert between logarithmic and exponential forms.
  2. The properties of logarithms (product, quotient, power rules).
  3. How to solve logarithmic equations.
  4. Why logarithms are used in real-world applications.
  5. Exploring logarithms to different bases (e.g., base 10, natural logarithms).

Tip: When solving logarithmic problems, always try to express the number in terms of powers of the base to simplify the process!

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponentiation

Formulas

log_b(a) = x, if a = b^x

Theorems

Logarithmic identity: log_b(b^x) = x

Suitable Grade Level

Grades 7-9