Next, we simplify further by expanding the terms using the properties of exponents.
(2^x)^x + 4^x - 3 = 2^(-x) * 2^(2x) - 4
2^(x^2) + 2^(2x) - 3 = 2^(2x-x) - 4
2^(x^2) + 2^(2x) - 3 = 2^x - 4
Now, we have the equation in terms of powers of 2. To solve this equation, we can try to simplify further or use numerical methods to find the value of x.
To solve this equation, we will first simplify it by using the properties of exponents.
Given equation: (2^x+4)^x - 3 = 0.5^x * 4^x - 4
Now, we know that 4 can be written as 2^2. So we will rewrite 4^x as (2^2)^x = 2^(2x).
Therefore, the equation becomes: (2^x+4)^x - 3 = (0.5^x * 2^(2x)) - 4
Next, we simplify further by expanding the terms using the properties of exponents.
(2^x)^x + 4^x - 3 = 2^(-x) * 2^(2x) - 4
2^(x^2) + 2^(2x) - 3 = 2^(2x-x) - 4
2^(x^2) + 2^(2x) - 3 = 2^x - 4
Now, we have the equation in terms of powers of 2. To solve this equation, we can try to simplify further or use numerical methods to find the value of x.