Use the like bases property to solve the equation \( 64^{x}=1024 \) \( x=\square \)

To solve the equation \( 64^{x} = 1024 \), we start by expressing both numbers as powers of the same base. Notably, both 64 and 1024 can be expressed as powers of 2: - \( 64 = 2^6 \) - \( 1024 = 2^{10} \) Now we can rewrite the equation using these bases: \((2^6)^{x} = 2^{10}\) Using the property of exponents \((a^{m})^{n} = a^{mn}\), we get: \(2^{6x} = 2^{10}\) Since the bases are the same, we can set the exponents equal to each other: \(6x = 10\) Now, we solve for \(x\): \(x = \frac{10}{6} = \frac{5}{3}\) So, the solution is: \(x = \frac{5}{3}\)