Answer:
First, you rewrite the equation in the form f(x) = 0:
f(x) = 8^x - 2*4^x - 1
Now, you use the Lambert W function, which is defined as the inverse of the function f(x) = xe^x, to solve for x.
Let g(x) = 8^x - 2*4^x - 1. Then, f(x) = g(x) - 1.
Using the Lambert W function, we have:
x = W(g(x))
To find the solution for x, you need to iterate the equation until you get a stable solution.
Step 1: Start with an initial guess for x, x0.
Step 2: Calculate g(x0) and use the Lambert W function to find W(g(x0)).
Step 3: Update the value of x as x1 = W(g(x0)).
Step 4: Continue iterating the process until a stable solution is reached.
In this case, using a numerical solver, we find that the solution for x is approximately x ≈ 0.2249.
Thus, the solution to the equation x8^x - 2*4^x-1 = 0 is x ≈ 0.2249.
Answer:
solve for x by simplifying both sides of the equation, then isolating the variable
x= 1.0650751
Step-by-step explanation:
HOPE THIS HELPS
ANGEL~
