Write log 1,024^16=25 in exponential form.

Answer 1

IF this is the common log, then it's base = 10

and 10^25 = 1,024^16

but "log" also is often used to mean a base e, even though we're accustomed to seeing that as "ln"

if "log" means the natural base e, then e^25=1.024^16

Or maybe you might have intended to use 1,024 as the base, but 1,024^25 doesn't =16, so that seems unlikely

in less advanced mathematics, log means common log, with base 10, so go with the first above, and rewrite the log in exponential form as 10^25 = 1,024^16. Still, 10^25 is 1 with 25 zeroes after it: 10000.....000 which ends in 0. While 1,024^16 will end in 6. or more accurately, 1.2676506 x 10^30 > 10^25, So they aren't equal either. same with the natural log, e^25 doesn't = 1,024^16

1,024 = 2^10, and (2^10)^16 = 2^160 might have something to do with why they came up with this problem, or what might be missing from the problem.