Which of the following is equivalent to $2 \ln (10 x)$ for $x> 0$ ?
Choose the correct answer below.
$\ln 100+\ln x$
$\ln (20 x)$
$\ln 20+\ln x$
$\ln \left(100 x^{2}\right)$

Answer

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Answer

$\boxed{\ln \left(100 x^{2}\right)}$ is the final answer.

Steps

Step 1 ：Given the expression $2 \ln (10 x)$ for $x>0$.

Step 2 ：Using the property of logarithms that states $n \ln a = \ln a^n$, we can rewrite the given expression as $\ln (10x)^2$.

Step 3 ：This simplifies to $\ln (100x^2)$.

Step 4 ：So, the equivalent expression to $2 \ln (10 x)$ for $x>0$ is $\ln \left(100 x^{2}\right)$.

Step 5 ：$\boxed{\ln \left(100 x^{2}\right)}$ is the final answer.