Math Problem Statement
What is the value of
log
2
1
/32
?
Solution
To find the value of , we can break it down step by step.
Step 1: Express 32 as a power of 2
We know that: So, we can rewrite the expression as:
Step 2: Apply the logarithmic property for division
Using the property of logarithms , we get:
Step 3: Simplify using the logarithmic identity
Since , the expression becomes:
Thus, the value of is -5.
Would you like more details on logarithmic properties, or have any other questions?
Related questions:
- How do you calculate ?
- What is the change of base formula for logarithms?
- Can you simplify ?
- How does the power rule for logarithms work?
- What is the inverse of a logarithmic function?
Tip:
To calculate logarithms easily, remember the basic powers of 2, 3, and other common bases.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Exponents
Logarithmic Properties
Formulas
log_b(1/x) = -log_b(x)
log_b(b^x) = x
Theorems
Logarithmic properties
Logarithmic identities
Suitable Grade Level
Grades 7-9