## Intermediate Algebra: Connecting Concepts through Application

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