Evaluate the given logarithm. 3 2 log 1 \frac32\log1 2 3 lo g 1

In this problem, we're asked to evaluate the given logarithm. And here I have 3 halves times log of 1. Now we know that log by itself is the common log, so this is really log base 10. But the log of 1, no matter what the base is, is always going to be 0 based on this property that we know here. So this is really just threetwo times 0, which anything times 0 is just 0. So my final answer here is that threetwo times the log of 1 is just 0. Let me know if you have any questions.

0. Functions

Properties of Logarithms

Business Calculus

0. Functions

Properties of Logarithms

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Multiple Choice

Evaluate the given logarithm.
$\frac32\log1$

$\frac32$

$0$

$1$

$10$

Verified step by step guidance

Step 1: Recognize the problem involves evaluating a logarithmic expression. The given expression appears to be improperly formatted. Let's clarify it as $ \log_{32}(1) $, which means the logarithm of 1 with base 32.

Step 2: Recall the logarithmic property $ \log_b(1) = 0 $ for any base $ b > 0 $. This is because any number raised to the power of 0 equals 1, i.e., $ b^0 = 1 $.

Step 3: Apply the property to the given expression. Since the base is 32 and the argument is 1, the result of $ \log_{32}(1) $ is 0.

Step 4: Verify the result conceptually. The logarithm asks, 'To what power must 32 be raised to result in 1?' The answer is 0, as $ 32^0 = 1 $.

Step 5: Conclude that the value of the logarithmic expression is 0, and select the corresponding answer from the provided options.