Certainly! Let's solve the problem using the provided Mathjax formatting:

Given \(34_n = 10011_2\), we want to find the value of \(n\).

Converting \(34_n\) to base 10:

\[34_n = 3 \cdot n^1 + 4 \cdot n^0\]

Converting \(10011_2\) to base 10:

\[10011_2 = 1 \cdot 2^4 + 0 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0\]

Setting the two expressions equal to each other:

\[3n + 4 = 16 + 2 + 1\]

Simplifying the equation:

\[3n + 4 = 19\]

Subtracting 4 from both sides:

\[3n = 15\]

Dividing both sides by 3:

\[n = 5\]