in general, how do i go about solving log inequalities?

Question

turingtest · Answer

general question are hard in math...
ideas:
- get logs to be the same base
- combine as many log expressions under one log sign as possible
- raise the base of the log to the power of both sides to get rid of the log
this is subject to the particular situation though, so some things will not work at times

anonymous · Answer

can u give an example, i know extremely general but it would help haha

turingtest · Answer

$$\log_2x+2\log_2x=\log_48$$get the bases the same...

turingtest · Answer

$$\log_2x+\log(x^2)=\frac{\log_28}{\log_24}$$combine the x's under one log sign...

turingtest · Answer

$$\log_2(x^3)=\frac32$$raise the base (2) to the power of both sides...

turingtest · Answer

$$\large x^3=2^{\frac32}$$now just solve like normal...$$x=(2^\frac32)^{\frac13}=2^{\frac12}=\sqrt2$$cool, the problem I made up had a nice answer :D