When you are working with equations with indices, try to
either rarr " make the bases the same"→ make the bases the same
or rarr " make the indices the same"→ make the indices the same
0.5 = 1/20.5=12 This is a better form to use, because you should recognise that 16 is one of powers of 2.......
rarr2^4 = 16 and 2^8 = 16^2→24=16and28=162
(1/2)^x = 16^2(12)x=162
(1/2)^x = 2^8(12)x=28
2^-x = 2^8 " " rarr "one of the index laws: "(a/b)^m = (b/a)^-m2−x=28 →one of the index laws: (ab)m=(ba)−m
Now the bases are the same so we have:
-x = 8 hArr x = -8−x=8⇔x=−8
