Math Problem Statement

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Part 1

Write as a logarithmic equation.

5 cubed53equals=125125

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Part 1

The logarithmic form is

enter your response here.

​(Use integers or fractions for any numbers in the​ expression.)

Solution

To rewrite the equation 53=1255^3 = 125 in logarithmic form, we use the definition of a logarithm:

If ab=ca^b = c, then the equivalent logarithmic form is loga(c)=b\log_a(c) = b.

For 53=1255^3 = 125, the base aa is 5, the result cc is 125, and the exponent bb is 3.

So, the logarithmic form is:

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

Let me know if you'd like more details or if you have any questions!


Related Questions

  1. What is the logarithmic form of 24=162^4 = 16?
  2. How would you write 102=10010^2 = 100 in logarithmic form?
  3. Can you convert 72=497^2 = 49 into logarithmic form?
  4. How do you express 34=813^4 = 81 in logarithmic form?
  5. Rewrite 62=366^2 = 36 as a logarithmic equation.

Tip: Remember, in the equation ab=ca^b = c, the logarithmic form will be loga(c)=b\log_a(c) = b.

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Math Problem Analysis

Mathematical Concepts

Exponents
Logarithms

Formulas

If a^b = c, then log_a(c) = b

Theorems

Definition of logarithms

Suitable Grade Level

Grades 8-10