Answer
$3$ $log$ ${2}$ + $\frac{3}{2}$ $log$ ${x}$ - $3$ $log$ ${5}$
Work Step by Step
Use the Power Property of Logarithms to rewrite this expression. The property states that $log_b$ ${m^n}$ = $n$ $log_b$ ${m}$:
$3$ $log$ $\frac{2\sqrt {x}}{5}$
Use the Quotient Property of Logarithms. According to this property, $log_b$ ${m}$ - $log_b$ ${n}$ = $log_b$ $\frac {m}{n}$:
$3$ $log$ ${2\sqrt {x}}$ - $3$ $log$ ${5}$
Use the Product Property of Logarithms. According to this property, $log_b$ ${mn}$ = $log_b$ ${m}$ + $log_b$ ${n}$:
$3$ $log$ ${2}$ + $3$ $log$ ${\sqrt {x}}$ - $3$ $log$ ${5}$
Convert the radical term to an exponential one:
$3$ $log$ ${2}$ + $3$ $log$ ${x^{\frac{1}{2}}}$ - $3$ $log$ ${5}$
Use the Power Property of Logarithms to rewrite this expression. The property states that $log_b$ ${m^n}$ = $n$ $log_b$ ${m}$:
$3$ $log$ ${2}$ + $\frac{3}{2}$ $log$ ${x}$ - $3$ $log$ ${5}$
