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

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

Identify the expression that needs to be evaluated: $ \log_{\frac{3}{2}} \left( \frac{32}{23} \right) $.

Recall the change of base formula for logarithms: $ \log_b a = \frac{\log_c a}{\log_c b} $, where $ c $ is a base of your choice, often 10 or $ e $.

Apply the change of base formula to the given logarithm: $ \log_{\frac{3}{2}} \left( \frac{32}{23} \right) = \frac{\log \left( \frac{32}{23} \right)}{\log \left( \frac{3}{2} \right)} $.

Calculate $ \log \left( \frac{32}{23} \right) $ and $ \log \left( \frac{3}{2} \right) $ using a calculator or logarithm tables.

Divide the result of $ \log \left( \frac{32}{23} \right) $ by $ \log \left( \frac{3}{2} \right) $ to find the value of the original logarithm expression.