To solve the expression \( \frac{7^x}{7^5} = 7^{12} \), we can use the property of exponents that states:
\[ \frac{a^m}{a^n} = a^{m-n} \]
Applying this to the left side of the equation:
\[ \frac{7^x}{7^5} = 7^{x-5} \]
Now, we can set the exponents equal to each other, since the bases (7) are the same:
\[ x - 5 = 12 \]
To solve for \( x \), add 5 to both sides:
\[ x = 12 + 5 \] \[ x = 17 \]
The missing number is \( 17 \).