Answer
$2000=x$
Work Step by Step
We are asked to solve:
$\log{x}-\log{2}=3$
Recall the quotient property of logarithms (pg. 462):
$\log_b{\frac{m}{n}}=\log_b{m}-\log_b{n}$
Applying this property to our equation, we get:
$\log{\frac{x}{2}}=3$
Next, recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation $\left(\text{with }b=10, y=3, x=\frac{x}{2}\right)$, we get:
$10^3=\frac{x}{2}$
$1000=\frac{x}{2}$
$2000=x$
