Would someone please list all the rules regarding logaritmic inequalities.

Question

lgbasallote · Answer

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

anonymous · Answer

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

lgbasallote · Answer

but that's just rule of inequality

lgbasallote · Answer

you change the sign when you divide by -1

lgbasallote · Answer

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

lgbasallote · Answer

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

lgbasallote · Answer

that's when you change signs

anonymous · Answer

$$0.06^{x}<0.001$$ok... so how would you solve this...

anonymous · Answer

how is the inequality sign changed?

lgbasallote · Answer

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

anonymous · Answer

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

lgbasallote · Answer

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?

lgbasallote · Answer

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

lgbasallote · Answer

i just turned it into log form

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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