C. He defeated the Axis armies of Italy and Germany at El Alamein, Egypt.
D. He defeated the German army at the Battle of the Bulge.
Answer:
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Explanation:
The property that must be used in all the proofs is: logb(b^y) =y
<h3>What are the proofs or rules of logarithms?</h3>
The proofs are statements that are used to validate or invalidate a logarithmic expression
There are several proofs of logarithms; some of them are:
- Product rule
- Quotient rule
- Power rule
- Change of base
The common property in the first three proofs (listed above) is:
This is so because, it links all the three proofs
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The matrix is a 2 by 2 matrix, and the determinant of the matrix by hand is -3
<h3>How to determine the determinant?</h3>
The matrix is given as:
1 2
2 1
The determinant of the matrix is calculated using the following product expression
det |A| = 1 * 1 - 2 * 2
Evaluate the product
det |A| = 1 - 4
Evaluate the difference
det |A| = -3
Hence, the determinant of the matrix by hand is -3
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