Question

solve. write your answer as an integer or a fraction in simplest form.
$4^{2x} = 64$
$x = \boxed{\frac{\square}{\square}}$

Explanation:

Step1: Express 64 as a power of 4

We know that \(4^3 = 64\), so the equation \(4^{2x}=64\) can be rewritten as \(4^{2x}=4^3\).

Step2: Set the exponents equal

Since the bases are the same (both are 4) and the exponential function is one - to - one, we can set the exponents equal to each other. That is, \(2x = 3\).

Step3: Solve for x

To solve for \(x\), we divide both sides of the equation \(2x = 3\) by 2. So \(x=\frac{3}{2}\).

Answer:

\(\frac{3}{2}\)