TRY THIS EXPONENTIAL EQUATION
4(2^Xsquare)=8^X
To solve the exponential equation 4(2^x^2) = 8^x, we can start by simplifying the equation.
Let's rewrite each side of the equation using the same base. In this case, we can rewrite 8^x as (2^3)^x.
4(2^x^2) = (2^3)^x
Next, apply the properties of exponents. When we raise a power to another power, we multiply the exponents.
4(2^x^2) = 2^3x
Now, let's simplify further. Since we have the same base on both sides of the equation, we can equate the exponents.
x^2 = 3x
Now we have a quadratic equation. Let's rearrange it to solve for x.
x^2 - 3x = 0
Factor out x from both terms:
x(x - 3) = 0
From here, we have two possibilities for the value of x:
1. x = 0 (satisfies x(x - 3) = 0)
2. x - 3 = 0, which implies x = 3
So the possible solutions for the equation 4(2^x^2) = 8^x are x = 0 and x = 3.