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

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Answer 1 · 2017-02-19T01:37:17

$x >= 7$

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:

$x >= 7$

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