Math Problem Statement

Rewrite the exponential equation 5^3 = 125 in logarithmic form.

Solution

To convert the given exponential equation into logarithmic form, we start from the statement:

53=1255^3 = 125

In exponential form, this means that the base b=5b = 5, the exponent y=3y = 3, and the result x=125x = 125. To rewrite this in logarithmic form, we use the relationship:

y=logb(x)y = \log_b(x)

Substituting the values:

3=log5(125)3 = \log_5(125)

Therefore, the logarithmic form of 53=1255^3 = 125 is:

log5(125)=3\log_5(125) = 3

This is the answer that should go in the blank box.

Would you like further details or explanations?

Here are five related questions you might find useful:

  1. What is the logarithmic form of 24=162^4 = 16?
  2. How do you convert from logarithmic to exponential form?
  3. What are the properties of logarithms that can simplify calculations?
  4. How do you evaluate log2(8)\log_2(8)?
  5. What is the natural logarithm and how does it differ from other logarithms?

Tip: Remember that logarithms are the inverse operation of exponentiation, meaning they "undo" exponents.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents

Formulas

x = b^y if and only if y = log_b(x)

Theorems

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Suitable Grade Level

Grades 9-10