To solve the expression \( \frac{7^x}{7^5} = 7^{12} \), we can use the properties of exponents.
First, we know that when we divide two numbers with the same base, we can subtract the exponents:
\[ \frac{7^x}{7^5} = 7^{x-5} \]
So we can rewrite the equation as:
\[ 7^{x-5} = 7^{12} \]
Since the bases are the same, we can set the exponents equal to each other:
\[ x - 5 = 12 \]
To solve for \(x\), add 5 to both sides:
\[ x = 12 + 5 \]
\[ x = 17 \]
Therefore, the missing number is \( \boxed{17} \).
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