Answer
$2\log_3$ ${2}$ - $2$ $\log_3$ ${x}$
Work Step by Step
Evaluate the exponential expression first:
$\log_3 {4x^{2}}$
Use the Quotient Property of Logarithms. According to this property, $\log_b$ ${m}$ - $\log_b$ ${n}$ = $\log_b$ $\frac {m}{n}$. Thus, the given expression is equivalent to:
$\log_3$ ${4}$ - $\log_3$ ${x^{2}}$
$=\log_3$ ${2^2}$ - $\log_3$ ${x^{2}}$
Use the Power Property of Logarithms to rewrite this expression. The property states that $\log_b$ ${m^n}$ = $n$ $\log_b$ ${m}$. Thus, the expression above is equivalent to:
$2\log_3$ ${2}$ - $2$ $\log_3$ ${x}$
