Final answer:
To solve the exponential equation 9x - 3 = 729, rewrite it as (3^2)^(3x) - 3 = 729. Simplify it to 3^(6x) - 3 = 729. Rewrite 729 as 3 cubed, then set 6x = 3 and solve for x to find x = 1/2.
Step-by-step explanation:
To solve the exponential equation 9x - 3 = 729, we need to rewrite it as an equivalent equation. Since 729 is equal to 9 cubed, we can write the equation as (3^2)^(3x) - 3 = 729. Applying the rule of cubing exponentials, we can simplify it further to 3^(6x) - 3 = 729. Now, we can rewrite 729 as 3 cubed, so the equation becomes 3^(6x) - 3 = 3^3. Since the bases are the same, the exponents must be equal, so we can set 6x = 3. Solving for x, we find x = 1/2. Therefore, the equation equivalent to 9x - 3 = 729 is not given in the options provided.