Math Problem Statement

Write the equation 81 = 9^2 in logarithmic form.

Solution

To express the equation 81=9281 = 9^2 in logarithmic form, recall that the general form of a logarithmic equation is:

logb(a)=c\log_b(a) = c

Where bb is the base, aa is the result, and cc is the exponent. In this case, 92=819^2 = 81 can be written in logarithmic form as:

log9(81)=2\log_9(81) = 2

So, the logarithmic form of the given equation is:

log9(81)=2\log_9(81) = 2

Let me know if you need further clarification or have any more questions!

Here are 5 related questions you may find helpful:

  1. How do you convert other exponential equations to logarithmic form?
  2. What is the inverse relationship between logarithms and exponents?
  3. How do you solve logarithmic equations?
  4. What are the properties of logarithms?
  5. Can logarithms be used to simplify equations involving large exponents?

Tip: Always make sure the base and the result in the logarithmic form match the base and result in the exponential form!

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Math Problem Analysis

Mathematical Concepts

Exponents
Logarithms
Base-Exponent Relationships

Formulas

log_b(a) = c ⇔ b^c = a

Theorems

Logarithmic-Exponential Relationship

Suitable Grade Level

Grades 8-10