Question

How do you write an equation of a line going through `(1/2)^x =16^2`?

Answer 1

`x=-8`

Explanation:

`1/2=2^(-1)`

`rArr (1/2)^x=((2)^(-1))^x=2^(-x)`

`16=2^4`

`rArr 16^2 = (2^4)^2=2^8`

Therefore
`color(white)("XXX")(1/2)^x=16^2`

`rArr 2^(-x) = 2^8`

`rArr x=-8`