Question

How do you solve the exponential inequality `8^(2x)>=8^(x+7)`?

Answer 1

`x >= 7`

Explanation:

Note that the function `f(x) = 8^x` is a strictly monotonically increasing - and therefore one to one - function from `(-oo, oo)` to `(0, oo)`.

So:

`8^(2x) >= 8^(x+7) <=> 2x >= x+7`

Subtract `x` from both sides of the simplified inequality to find:

`x >= 7`