Solve for x: log2 (4^x) = 16

Answer 1

I assume you mean this:

log₂ (4^x) = 16 (read the left side as "log to base 2 of 4^x")

The log of a number is the exponent applied to the base to get that number. Thus, the equivalent equation is:

2^16 = 4^x

2^16 = 4^8, so we have: 4^8 = 4^x, and therefore x = 8

CHECK:

log₂ (4^8) = 8 * log₂4 = 8 * 2 = 16