Given that log 2 = 0.3010 and log 3 = 0.4771, find the value of log(1.5)".

To find the value of $\log(1.5)^2$, we will use the given values $\log 2 = 0.3010$ and $\log 3 = 0.4771$ and logarithm properties.

Step 1: Rewrite $1.5$ as a fraction. $1.5 = \frac{15}{10} = \frac{3}{2}$

Step 2: Apply the logarithm power rule, $\log(a^b) = b \log a$. $\log(1.5)^2 = 2 \log(1.5)$

Step 3: Substitute the fractional form of $1.5$ and apply the logarithm quotient rule, $\log\left(\frac{a}{b}\right) = \log a - \log b$. $2 \log(1.5) = 2 \log\left(\frac{3}{2}\right) = 2 (\log 3 - \log 2)$

Step 4: Substitute the given values for $\log 3$ and $\log 2$. $2 (0.4771 - 0.3010)$

Step 5: Perform the subtraction and multiplication. $2 (0.1761) = 0.3522$

The value of $\log(1.5)^2$ is $0.3522$. This matches option A.

The final answer is $\boxed{A. 0.3522}$.

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