Rodney's current savings account can be represented by the expression 9^8-x . His brother's savings account can be represented by the expression 27^x-3 Their accounts are compounding yearly After how many years will their accounts have the same amount of money? (1)/(5)years 5 years -5years

To solve this problem, we need to find the value of x that makes the two expressions equal.<br /><br />Given:<br />Rodney's savings account: $9^{8-x}$<br />His brother's savings account: $27^{x-3}$<br /><br />We want to find the value of x when the two accounts have the same amount of money.<br /><br />Step 1: Set the two expressions equal to each other.<br />$9^{8-x} = 27^{x-3}$<br /><br />Step 2: Rewrite the expressions with the same base.<br />$9^{8-x} = (3^3)^{x-3}$<br />$9^{8-x} = 3^{3(x-3)}$<br /><br />Step 3: Rewrite the expression with the same base.<br />$9^{8-x} = 3^{3x-9}$<br /><br />Step 4: Rewrite the expression with the same base.<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{3x-9}$<br />$9^{8-x} = 3^{