Would someone please list all the rules regarding logaritmic inequalities.
sorry ... i needed to know the rules for logaritmic INEQUALITIES (i.e. when does the inequality sign switch around)
but that's just rule of inequality
you change the sign when you divide by -1
or example x > 1 since x is already positive no need to change signs
however -x >1 you need to make x positive so divide by -1 x < -1
that's when you change signs
\[0.06^{x}<0.001\]ok... so how would you solve this...
how is the inequality sign changed?
\[\log_{0.06} 0.001 < x\] are you sure there's a change of sign there?
not sure... can you please lead me through it
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?
btw...i did nothing fancy in \[\log_{0.06} 0.01 < x\]
i just turned it into log form
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.
so in this case would that be the 0.06 or the 0.001 which caused the sign to switch around?
Sorry for the late reply. Both of it would. You can experiment the values after log on your calculator.
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