How do you solve the exponential inequality $3^(x-2)<=3^(2x+4)$ ?

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Answer 1 · 2017-06-13T17:08:56

Given: $3^(x-2)<=3^(2x+4)$

Use the base 3 logarithm on both sides:

$log_3(3^(x-2))<=log_3(3^(2x+4))$

This makes both the logarithm and the 3 disappear:

$x-2<=2x+4$

Subtract x from both sides:

$-2<=x+4$

Subtract 4 from both sides:

$-6<=x$

How do you solve the exponential inequality 3^(x-2)<=3^(2x+4)3^(x-2)<=3^(2x+4)?