Math Problem Statement
Solution
To solve the problem, let's break it down step by step:
Problem Statement
Given:
We need to find .
Solution
Since , this implies that is the inverse of . Therefore, .
Now, to find , we need to determine the value of such that:
Given:
Set and solve for : Subtract 2 from both sides: Now, exponentiate both sides to remove the logarithm: Subtract 1 from both sides:
So, .
Final Answer
Do you want details or have any questions?
Here are 8 related questions:
- How do you find the inverse of a logarithmic function in general?
- What are the properties of inverse functions?
- Why does the equation imply that is the inverse of ?
- How do you solve equations involving natural logarithms and exponents?
- What is the significance of the constant "2" in the function ?
- Can have more than one inverse?
- What is the domain of the function ?
- How do you graph and its inverse function?
Tip: Understanding how logarithmic and exponential functions are inverses of each other is key to solving problems involving these functions.
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Math Problem Analysis
Mathematical Concepts
Functions
Inverse Functions
Logarithmic Functions
Exponential Functions
Formulas
Inverse function formula
Theorems
Properties of inverse functions
Suitable Grade Level
Grades 11-12