Answer
$x=\frac{5}{8}$
Work Step by Step
Apply the quotient property for logarithms to have:
$\log_4{(\frac{10}{x})}=2$
RECALL:
$\log_a{b}=x \longrightarrow a^x=b$
Use this rule in converting the equation to its equivalent exponential equation to have:
$4^2=\frac{10}{x}
\\16=\frac{10}{x}
\\16(x)=10
\\x=\frac{10}{16}
\\x=\frac{5}{8}$
