Final answer:
The equation 8^x = 4^(x+1) is solved by rewriting both sides with a common base of 2, leading to the equation 2^(3x) = 2^(2x+2), and subsequently solving for x, which gives x = 2.
Step-by-step explanation:
To solve the equation with exponential terms, we need to rewrite both sides with a common base. We have the equation 8x = 4x+1. Notice that both 8 and 4 are powers of 2 (8 = 23 and 4 = 22). We can rewrite the equation as (23)x = (22)x+1.
By the properties of exponents, we have 23x = 22x+2. Since the bases are now the same, we can set the exponents equal to each other, which gives us the simple equation 3x = 2x + 2.
Subtracting 2x from both sides, we get x = 2. Thus, the solution of the original equation is x = 2.