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#