7 to the power of ? divided by 7 to the power of 5 equals 7 to the power of 12

1 answer

To solve the equation:

\[ \frac{7^x}{7^5} = 7^{12} \]

we can use the properties of exponents. When you divide exponential terms with the same base, you subtract the exponents:

\[ 7^{x - 5} = 7^{12} \]

Since the bases are the same, we can set the exponents equal to each other:

\[ x - 5 = 12 \]

Solving for \(x\):

\[ x = 12 + 5 \] \[ x = 17 \]

So, the solution is:

\[ \boxed{17} \]