Math Problem Statement
What is the value of x when \(x = 2 \log_5 1 + \log_3 81\)?
Solution
The problem in the image asks for the value of when:
Let's break it down step by step.
Step 1: Simplify the expression
The logarithm of 1 in any base is 0, so:
Thus, the first term becomes:
Step 2: Simplify
We need to express 81 as a power of 3. Since , we have:
Step 3: Combine the results
The equation now simplifies to:
Therefore, the value of is .
Would you like more details or have any questions? Here are some related questions you might find interesting:
- How do you evaluate logarithms with different bases?
- What are the properties of logarithms that are useful in simplifying expressions?
- How can you convert logarithms to a different base using the change of base formula?
- What is the significance of logarithms in real-world applications?
- How would you solve an equation involving a sum of logarithms with different bases?
Tip: Remember that the logarithm of 1 is always 0, regardless of the base, because any number raised to the power of 0 equals 1.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Algebra
Exponents
Formulas
\(\log_b 1 = 0\)
\(\log_b (a^n) = n \cdot \log_b a\)
Theorems
Logarithm properties
Exponentiation properties
Suitable Grade Level
Grades 10-12