Answer
$\log(5\cdot 2)\ne\log{5}\cdot \log{2}$ because $\log{(5\cdot 2)} = \log{5}+\log{2}$
Work Step by Step
We are asked to explain the following expression:
$\log(5\cdot 2)\ne \log{5}\cdot \log{2}$
Recall the product property of logarithms (pg. 462):
$\log_b{mn}=\log_b{m}+\log_b{n}$
If we apply the product rule to the left expression, we get:
$\log(5\cdot 2)=\log{5}+\log{2}\ne\log{5}\cdot \log{2}$
Thus we see that the source of the error is the "times" sign in between the logarithms, which should instead be a "plus" sign (as per the product property).
