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Mathematics 12 Online
OpenStudy (anonymous):

Would someone please list all the rules regarding logaritmic inequalities.

OpenStudy (lgbasallote):

will this help: http://openstudy.com/updates/4fa45f8fe4b029e9dc34e0b5

OpenStudy (anonymous):

sorry ... i needed to know the rules for logaritmic INEQUALITIES (i.e. when does the inequality sign switch around)

OpenStudy (lgbasallote):

but that's just rule of inequality

OpenStudy (lgbasallote):

you change the sign when you divide by -1

OpenStudy (lgbasallote):

or example x > 1 since x is already positive no need to change signs

OpenStudy (lgbasallote):

however -x >1 you need to make x positive so divide by -1 x < -1

OpenStudy (lgbasallote):

that's when you change signs

OpenStudy (anonymous):

\[0.06^{x}<0.001\]ok... so how would you solve this...

OpenStudy (anonymous):

how is the inequality sign changed?

OpenStudy (lgbasallote):

\[\log_{0.06} 0.001 < x\] are you sure there's a change of sign there?

OpenStudy (anonymous):

not sure... can you please lead me through it

OpenStudy (lgbasallote):

you'll have a change in sign for example: \[\large 16^{-x} > 3\] \[\large \log_{16} 3 > -x\] \[\large -\log_{16} 3 < x\] do you see that?

OpenStudy (lgbasallote):

btw...i did nothing fancy in \[\log_{0.06} 0.01 < x\]

OpenStudy (lgbasallote):

i just turned it into log form

OpenStudy (anonymous):

All you need to know is that when you log a number less than 1, it has a negative value and hence, you must revert the inequality sign when moving the log number over.

OpenStudy (anonymous):

so in this case would that be the 0.06 or the 0.001 which caused the sign to switch around?

OpenStudy (anonymous):

Sorry for the late reply. Both of it would. You can experiment the values after log on your calculator.

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