9 ^ (4 ^ (x - 2)) = 81 ^ (2 ^ (x - 3))

Answer 1

To solve the equation 9^(4^(x-2)) = 81^(2^(x-3)), we need to simplify both sides of the equation.

First, let's simplify 9^(4^(x-2)):
9^(4^(x-2)) = 3^2^(4^(x-2)) = 3^(2 * 4^(x-2)) = 3^(8^(x-2))

Now let's simplify 81^(2^(x-3)):
81^(2^(x-3)) = 3^4^(2^(x-3)) = 3^(4 * 2^(x-3)) = 3^(8^(x-3))

Since both sides of the equation are now in the same form, we can equate the exponents:

8^(x-2) = 8^(x-3)

Since both sides have the same base (8) and are equal, the exponents must be equal as well:

x - 2 = x - 3

Simplifying this equation gives us:

x = x - 1

This equation has no solution because x would have to be equal to x - 1, which is not possible. Therefore, there is no value of x that satisfies the original equation.