Math Problem Statement
Write the equation in its equivalent exponential form: 2 = log₄(16).
Solution
The given equation is .
To write this in its equivalent exponential form, we use the definition of logarithms:
Here:
- (the base),
- (the logarithm result),
- (the number).
Thus, the equivalent exponential form is:
Would you like further details or an explanation?
Related Questions
- What are some properties of logarithms and their equivalent exponential forms?
- How do you solve logarithmic equations using their exponential equivalents?
- Can you graph the exponential function and relate it to logarithms?
- What are the steps to simplify logarithmic expressions with different bases?
- How do logarithms apply to real-world exponential growth or decay problems?
Tip
Always remember: logarithms and exponents are inverse operations, making them extremely useful for solving equations involving either form!
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Math Problem Analysis
Mathematical Concepts
Logarithms
Exponents
Formulas
log_b(a) = c implies b^c = a
Theorems
Definition of a logarithm
Suitable Grade Level
Grades 8-10