Math Problem Statement
If log 27 = 1.431, then the value of log 9 is:
a. 0.934
b. 0.945
c. 0.958
d. 0.954
Solution
We are given that:
Our task is to find the value of .
First, express both 27 and 9 in terms of powers of 3:
Using the logarithmic identity:
We can express and as follows:
From , we know:
Solving for :
Now, substitute into the expression for :
Thus, the value of is:
Answer: d. 0.954
Do you have any questions or want more details on the steps?
Here are 5 questions to further explore logarithms:
- What is the logarithmic property that relates the logarithm of a product to individual logarithms?
- How would you find if you know ?
- What is the change of base formula for logarithms, and how is it used?
- How does the value of change if the base is 2 instead of 10?
- Can you explain why logarithms are useful in solving exponential equations?
Tip: When working with logarithms, always try to express the numbers in terms of powers of the same base for simpler calculations.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Algebra
Powers and Roots
Formulas
log(a^b) = b * log a
Theorems
Logarithmic Identity for Exponents
Suitable Grade Level
Grades 10-12