How do you solve an inequality where one side is a log and the other side does not equal 1?

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The way I worded the question probably wasn’t the best, sorry!
Example: #log_2x<-3#

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Answer 1 · 2018-01-24T07:27:38

#x<1/8#

You can apply pretty much the same method that you would use when solving an equation.

First, we begin by raising both sides as powers of two (to eliminate the #log_2#):
#log_2(x)<-3#

#cancel(2)^(cancel(log_2)(x))<2^-3#

#x<2^-3#

#x<1/2^3#

#x<1/8#