Math Problem Statement
The original handwritten problem shows the expressions \(\log_5 125\) and \(\log_2 8 = 3\).
Solution
The image contains mathematical expressions written in Arabic script, which translate to:
Explanation:
- The first expression is . To solve this, we find the power to which 5 must be raised to get 125. Since , .
- The second expression, , is already simplified. It states that the power to which 2 must be raised to get 8 is 3, since .
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Related Questions:
- What are the properties of logarithms?
- How do you convert between logarithmic and exponential forms?
- What are the laws of logarithms, such as the product, quotient, and power rules?
- How can you solve logarithmic equations with different bases?
- What are common logarithms and natural logarithms, and how are they used?
Tip: Always remember that is equivalent to . This helps in converting between logarithmic and exponential forms.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Exponential Functions
Formulas
\(\log_b a = c\) is equivalent to \(b^c = a\)
Simplifying logarithmic expressions
Theorems
Logarithmic and Exponential Relationship
Suitable Grade Level
Grades 8-10