Math Problem Statement
log4420+(log44)20−(log416)⋅(log464)
Solution
Let's break down the expression and solve it step by step.
You have the expression:
Step 1: Simplify
We know that for any base . Therefore:
Thus, the term becomes:
Step 2: Simplify
Recall that , so we can write:
Step 3: Simplify
Similarly, , so:
Step 4: Substitute back into the expression
Now, the expression becomes:
Step 5: Final Expression
Thus, the simplified expression is:
Now, unless you want to approximate , this is the simplified form. Would you like me to approximate or provide further details?
Related questions:
- How do you simplify logarithms with different bases?
- What are properties of logarithms that can help simplify expressions?
- How do you convert logarithms to different bases (e.g., from base 4 to base 10)?
- How do you simplify logarithmic expressions with exponents?
- Can you solve logarithmic equations by substitution?
Tip:
Remember that logarithms with the same base can be combined using the product, quotient, and power rules.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Properties of Logarithms
Logarithmic Simplification
Formulas
log_b(b) = 1
log_b(a^n) = n * log_b(a)
Theorems
Logarithm Product Rule
Logarithm Quotient Rule
Suitable Grade Level
Grades 9-11
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