Math Problem Statement
Solve log_4(x - 2) = 1.
Solution
To solve the given equation:
We proceed as follows:
Step 1: Convert logarithmic to exponential form
The general formula for converting logarithmic equations is:
Here, , , and . Applying the formula:
Step 2: Simplify the equation
Step 3: Solve for
Add 2 to both sides:
Final Answer:
The solution is . Therefore, the correct option is:
D. {6}
Would you like a detailed explanation of logarithms, or do you have further questions? Here are some related questions for practice:
- Solve .
- If , find .
- Rewrite the equation in exponential form.
- Explain the domain of .
- Solve .
Tip: Always ensure that the argument of the logarithmic function (e.g., ) is positive, as logarithms are undefined for non-positive values.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Exponential Equations
Formulas
log_b(a) = c ⟺ b^c = a
Theorems
Logarithmic to exponential conversion
Suitable Grade Level
Grades 9-11