To solve this inequality, we can start by rewriting it in a more manageable form:
9^(2x+1) + 13^(2x+1) <= 22*117^x
Since 117 = 9*13, we can rewrite the inequality as:
9^(2x+1) + 13^(2x+1) <= 22(913)^x
Next, let's simplify the right-hand side of the inequality:
22(913)^x = 229^x13^x
Now the inequality becomes:
9^(2x+1) + 13^(2x+1) <= 229^x13^x
Divide both sides by 9^x*13^x to get:
(9^(2x+1))/(9^x) + (13^(2x+1))/(13^x) <= 22
Now simplify the expression inside the parentheses:
9^(2x)9 / 9^x + 13^(2x)13 / 13^x <= 22
9^(x)9 + 13^x13 <= 22
Simplify further:
9^(x+1) + 13^(x+1) <= 22
Therefore, the inequality is:
This is the final form of the inequality.
To solve this inequality, we can start by rewriting it in a more manageable form:
9^(2x+1) + 13^(2x+1) <= 22*117^x
Since 117 = 9*13, we can rewrite the inequality as:
9^(2x+1) + 13^(2x+1) <= 22(913)^x
Next, let's simplify the right-hand side of the inequality:
22(913)^x = 229^x13^x
Now the inequality becomes:
9^(2x+1) + 13^(2x+1) <= 229^x13^x
Divide both sides by 9^x*13^x to get:
(9^(2x+1))/(9^x) + (13^(2x+1))/(13^x) <= 22
Now simplify the expression inside the parentheses:
9^(2x)9 / 9^x + 13^(2x)13 / 13^x <= 22
9^(x)9 + 13^x13 <= 22
Simplify further:
9^(x+1) + 13^(x+1) <= 22
Therefore, the inequality is:
9^(x+1) + 13^(x+1) <= 22
This is the final form of the inequality.