Answer
$16$
Work Step by Step
Step 1. Rewrite the equation $\frac{ln(x)}{ln2^4}+\frac{ln(x)}{ln2^2}+\frac{ln(x)}{ln2}=7 \longrightarrow ln(x)+2ln(x)+4ln(x)=28ln2 \longrightarrow ln(x)=4ln2 \longrightarrow x=2^4=16$
Step 2. Check, $x=16$ fits the original equation.
