Math Problem Statement
Solution
The equation shown is:
Steps to Solve Algebraically:
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Simplify the equation: Multiply through by to eliminate the fraction:
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Distribute the 5:
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Rearrange terms: Isolate :
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Solve for : Divide by 5:
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Take the natural logarithm (ln): Apply to both sides:
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Solve for :
Approximation:
Use a calculator to evaluate:
The provided answer is correct.
Would you like further explanation or clarifications? Here are some related questions to deepen your understanding:
- What properties of natural logarithms are important for solving exponential equations like this one?
- How does changing the constant (e.g., from 5 to another number) affect the solution process?
- Why is it necessary to isolate the exponential term before taking the natural logarithm?
- Can this equation be solved graphically, and how would the solution compare to the algebraic method?
- How can you verify the solution by substituting back into the original equation?
Tip: Always check your solution by plugging it back into the original equation to confirm it satisfies the problem!
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Logarithms
Formulas
Natural Logarithm: \(\ln(a)\)
Exponential equation manipulation
Theorems
Logarithmic Properties
Inverse Relationship between Exponentials and Logarithms
Suitable Grade Level
College-Level Algebra