Answer :
To solve the equation \( 9^{x-3} = 729 \), let's proceed step-by-step.
1. Express 729 as a base of 9:
\( 729 \) is a power of 9. We need to determine the exponent. It helps to know that:
[tex]\[ 9^3 = 729 \][/tex]
Therefore, we can rewrite 729 as:
[tex]\[ 729 = 9^3 \][/tex]
2. Rewrite the equation:
We substitute \( 729 \) with \( 9^3 \) in the original equation:
[tex]\[ 9^{x-3} = 9^3 \][/tex]
3. Compare the exponents:
Since the bases are the same (both sides are powers of 9), we can compare the exponents directly. This gives us:
[tex]\[ x - 3 = 3 \][/tex]
So, the equation \( 9^{x-3} = 729 \) is equivalent to \( 9^{x-3} = 9^3 \).
Thus, the correct answer is:
[tex]\[ \boxed{9^{x-3}=9^3} \][/tex]
This corresponds to the second option in the list of choices.
1. Express 729 as a base of 9:
\( 729 \) is a power of 9. We need to determine the exponent. It helps to know that:
[tex]\[ 9^3 = 729 \][/tex]
Therefore, we can rewrite 729 as:
[tex]\[ 729 = 9^3 \][/tex]
2. Rewrite the equation:
We substitute \( 729 \) with \( 9^3 \) in the original equation:
[tex]\[ 9^{x-3} = 9^3 \][/tex]
3. Compare the exponents:
Since the bases are the same (both sides are powers of 9), we can compare the exponents directly. This gives us:
[tex]\[ x - 3 = 3 \][/tex]
So, the equation \( 9^{x-3} = 729 \) is equivalent to \( 9^{x-3} = 9^3 \).
Thus, the correct answer is:
[tex]\[ \boxed{9^{x-3}=9^3} \][/tex]
This corresponds to the second option in the list of choices.
