Solving the Equation: 1/64 * 4^x * 2^x = 64
In this article, we will explore the solution to the equation 1/64 * 4^x * 2^x = 64. This equation involves exponential functions and requires a step-by-step approach to solve.
Simplifying the Equation
First, let's start by simplifying the equation. We can begin by rewriting the equation as:
$\frac{1}{64} * 4^x * 2^x = 64$
Next, we can rewrite the equation in exponential form:
$2^{-6} * 4^x * 2^x = 2^6$
Combining Like Terms
Now, let's combine like terms. We can rewrite the left-hand side of the equation as:
$2^{-6} * (2^2)^x * 2^x = 2^{-6} * 2^{2x} * 2^x$
Using the property of exponents, we can simplify this expression to:
$2^{-6} * 2^{3x} = 2^6$
Solving for x
Now, we can equate the exponents:
$-6 + 3x = 6$
Solving for x, we get:
$3x = 12$
$x = \boxed{4}$
Conclusion
Therefore, the solution to the equation 1/64 * 4^x * 2^x = 64 is x = 4.
