Math Problem Statement

Rewrite the expression log_3 81 = 4 in equivalent exponential form.

Solution

The expression given is log381=4\log_3 81 = 4. To rewrite this in exponential form, we can use the following relationship between logarithms and exponents:

logba=cis equivalent tobc=a\log_b a = c \quad \text{is equivalent to} \quad b^c = a

In this case:

  • The base bb is 3,
  • The result cc is 4,
  • And the number aa is 81.

Thus, the equivalent exponential form is:

34=813^4 = 81

Let me know if you'd like further details or clarifications!

Here are 5 related questions for further exploration:

  1. How do you convert an exponential equation to logarithmic form?
  2. What is the general form of an exponential function?
  3. How do you solve logarithmic equations with different bases?
  4. Can logarithmic functions be graphed easily? How would you graph y=log3xy = \log_3 x?
  5. What are some real-world applications of logarithms and exponential functions?

Tip: Always remember that logarithms and exponents are inverse functions of each other!

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Math Problem Analysis

Mathematical Concepts

Algebra
Logarithms
Exponents

Formulas

log_b a = c is equivalent to b^c = a

Theorems

Logarithmic-Exponential Inverse Relationship

Suitable Grade Level

Grades 8-10