Math Problem Statement
Simplify the logarithmic expression log(√(x³)√[³](y²) / z⁴).
Solution
The expression in the image is:
We can simplify this logarithmic expression using logarithmic properties. Let’s break it down step by step:
Step 1: Simplify the radicals
Thus, the expression becomes:
Step 2: Apply the logarithmic property for division
This gives:
Step 3: Apply the logarithmic property for multiplication
This gives:
Step 4: Apply the logarithmic power rule
Thus:
This is the simplified form of the given logarithmic expression.
Would you like further clarification on any step, or do you have other questions?
Related Questions:
- How can we apply these logarithmic properties to more complex expressions?
- What are the properties of logarithms that are most commonly used?
- How can the logarithmic power rule help in solving exponential equations?
- What happens if the logarithmic base is not specified in expressions?
- How does the change of base formula for logarithms work?
Tip:
When simplifying logarithmic expressions, always try to apply the power rule and product rule to break down complex terms into manageable parts.
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Math Problem Analysis
Mathematical Concepts
Algebra
Logarithmic Properties
Radicals
Formulas
log(A/B) = log(A) - log(B)
log(AB) = log(A) + log(B)
log(A^n) = n * log(A)
√(x³) = x^(3/2), ³√(y²) = y^(2/3)
Theorems
Logarithmic Rules
Suitable Grade Level
Grades 10-12