Answer
$x=0.25$
Work Step by Step
Recall the quotient property of logarithms (pg. 462):
$\log_b{\frac{m}{n}}=\log_b{m}-\log_b{n}$
Applying this property, we get:
$\log\frac{5}{2x}=1$
Now, recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=10, y=1, x=5/2x$), we get:
$10^{1}=\frac{5}{2x}$
$10(2x)=5$
$2x=\frac{5}{10}$
$2x=\frac{1}{2}$
$x=\frac{1}{4}=0.25$
We confirm that the answer works:
$\log 5-\log{(2\cdot0.25)}=1$
$\log 5-\log 0.5=1$
$\log{\frac{5}{0.5}}=1$
$\log{10}=1$
$1=1$
