Math Problem Statement
3log81+2log1/32
Solution
We will simplify the expression step by step.
Step 1: Use the logarithmic power rule
The power rule for logarithms states that . We apply this rule to both terms.
Step 2: Simplify the logarithmic terms
Now we calculate the values inside the logarithms:
So the expression becomes:
Step 3: Use the logarithmic addition rule
The addition rule for logarithms states that . We can now combine the two terms:
Step 4: Multiply the values inside the logarithm
Thus, the expression simplifies to:
This is the simplified form. If you need a decimal approximation, you can calculate , which is approximately .
Would you like more details or have any questions?
Here are 5 related questions:
- How can the power rule for logarithms help in simplifying logarithmic expressions?
- What is the relationship between logarithms and exponents?
- How can you use logarithms to solve equations involving exponential growth?
- What are the properties of logarithms that simplify complex expressions?
- Can logarithmic identities be used to evaluate expressions without a calculator?
Tip: Always remember to check the base of logarithms; if none is specified, it's usually base 10 (common logarithm).
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Math Problem Analysis
Mathematical Concepts
Logarithms
Properties of Logarithms
Formulas
Power Rule: a log b = log b^a
Addition Rule: log a + log b = log (a × b)
Theorems
Logarithmic Identities
Suitable Grade Level
Grades 10-12