#### Answer

The correct answer is
$x = \sqrt \frac{100}{3}$.
The student added $x$ to $3x$, when instead, she should be multiplying $x$ by $3x.$ Instead of obtaining $4x$, she should be obtaining $3x^{2}$.

#### Work Step by Step

$\log x + \log 3x = 2$
$\log 3x^{2} = 2$
$\log_{10} 3x^{2} = 2$
$10^{2} = 3x^{2}$
$100 = 3x^{2}$
$x^{2} = \frac{100}{3}$
$x = ±\sqrt \frac{100}{3}$
$x = \sqrt \frac{100}{3}$
The student added $x$ to $3x$, when instead, she should be multiplying $x$ by $3x.$ Instead of obtaining $4x$, she should be obtaining $3x^{2}$.