To solve the equation \( 7^? ÷ 75 = 7^{12} \), we can start by rewriting the left side of the equation:
\[ \frac{7^?}{75} = 7^{12} \]
Now, to isolate \( 7^? \), we can multiply both sides by \( 75 \):
\[ 7^? = 75 \cdot 7^{12} \]
Next, we can express \( 75 \) in terms of powers of \( 7 \) so we can factor out \( 7 \). However, since \( 75 \) cannot be expressed as a power of \( 7 \), let's write it in a product format:
This means we will need to find a solution by raising \( 7 \) to a power and multiplying by another factor.
Since we need to express both sides in the same base, we cannot easily express \( 75 \) using \( 7\). Thus, let's solve for \( ? \) without manipulating \( 75 \).
We can apply logarithmic properties here. Taking logarithms on both sides (base \( 7 \)):
\[ ? - \log_{7}(75) = 12 \]
Thus,
\[ ? = 12 + \log_{7}(75) \]
This indicates that as \( 75 \) is added in logarithmic terms, the exact numerical value of \( ? \) cannot be found without a calculator.
However, the main unknown is still represented as:
Assuming \( 75 \) can simply be a constant that keeps its logarithmic contribution minimal to the identity \( 75 \sim 49\) in relative logarithmic spaces, we get:
\[ ? = 12 + k \text{ (where \( k = \log_{7}(75)\))} \]
In conclusion, without actual calculation of the logarithmic terms, one simplified expression to express the missing number intuitively would be through terms simplifying processes.
2 can be represented succinctly in comparable terms if given a calculator or access to logarithm tabulation would yield \( ? \approx 13\).
For an exact numerical answer: The correct number \( ? \) cannot be stated without numerical approximation or logarithmic resolution. Complete logarithmic approaches provide additional analytical versatility. If needed exact numerical bounds can also be tabulated if assessed.
In summary, \( ? = 12 + \log_{7}(75) \) and is the most articulate answer that can be portrayed in exponential relationships retaining true integrity of logarithmic transformation.