Question
7 to the power of ? divided by 7 to the power of 5 equals 7 to the power of 12
Answers
GPT-4o mini
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:
\[
\boxed{17}
\]
\[
\frac{7^x}{7^5} = 7^{12}
\]
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:
\[
\boxed{17}
\]