Math Problem Statement
Solution
To solve the expression:
we proceed step-by-step using the logarithmic rules:
Step 1: Combine the terms using logarithmic properties
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Start with the first two terms:
Simplify inside the logarithm:
Therefore,
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For the third term, apply the power property:
Simplify the exponent:
Therefore:
Step 2: Combine all logarithms
The expression now becomes:
Using the logarithmic sum property:
Simplify the multiplication inside the logarithm:
Thus:
Final Answer:
The value of the expression is:
If you need further explanation or clarification, let me know!
Related Questions:
- How do you solve for general and ?
- What is the value of approximately?
- How can the power property of logarithms simplify terms like ?
- How do you combine logarithmic terms with fractions?
- What is the general form of a logarithmic equation?
Tip:
Always simplify logarithmic terms using properties like the product rule, quotient rule, and power rule before combining them. This saves time and reduces errors.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Logarithmic Properties
Algebraic Simplification
Formulas
Logarithmic Product Rule: \( \log_a(xy) = \log_a x + \log_a y \)
Logarithmic Quotient Rule: \( \log_a(\frac{x}{y}) = \log_a x - \log_a y \)
Logarithmic Power Rule: \( k \log_a x = \log_a(x^k) \)
Theorems
Properties of Logarithms
Suitable Grade Level
Grade 9-11
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