Final answer:
To solve the equation 16^(3x)=4^(x+2), rewrite the bases as powers of 2, apply the power property of exponents, equate the exponents, and solve for x.
Step-by-step explanation:
To solve the equation 16^(3x)=4^(x+2) we can start by expressing both bases as a power of 2. Since 16 = 2^4 and 4 = 2^2, we can rewrite the equation as (2^4)^(3x) = (2^2)^(x+2).
Next, we apply the power property of exponents. For the left side, we raise the base (2^4) to the power of 3x, resulting in 2^(4(3x)). For the right side, we raise the base (2^2) to the power of (x+2), resulting in 2^(2(x+2)).
Since the bases are the same, we can equate the exponents. Therefore, we have the equation 4*(3x) = 2*(x+2). Solving this equation will give us the value of x.
Learn more about Solving Exponential Equations