Solve for a: 32 a + 52 a - 62 a = 2 64

The equation is $3\log_2 a + 5\log_2 a - 6\log_2 a = \log_2 64$.
(Assuming 'a' is the argument for the logarithms on the left side, and $\log_2^{64}$ is a typo for $\log_2 64$).

Using the property $x \log_b y + z \log_b y = (x+z) \log_b y$:

Since the bases of the logarithms are the same, their arguments must be equal:

Take the square root of both sides:

Since the base of a logarithm must be positive, we take the positive root:

The final answer is 8.