Question

How do you solve `8^(2-x) = 4^(3x)`?

Answer 1

Express each side of the given equation with a base of `2`
then equating the exponents, solve for `x` to get
`color(white)("XXX")x=2/3`

Explanation:

`8^a = 2^(3a)`
`4^b = 2^(2b)`

Therefore
`color(white)("XXX")8^(2-x) = 4^(3x)`
is equivalent to
`color(white)("XXX")2^(6-3x)=4^(6x)`

Which implies
`color(white)("XXX")6-3x=6x`

`color(white)("XXX")9x = 6`

`color(white)("XXX")x=2/3`