I know the domain and range for \(f\left(x\right)=\log _6\left(\log _{\frac{1}{5}}\left(x\right)\right)\). However, I don't completely understand how that was achieved. Can someone please help me?

Guest Jan 24, 2022

#1**+1 **

Well for the first log_{1/5} portion, x has to be > 0 there are no logs of negative numbers...or log of zero so the domain goes from 0 < x < +inf

the corresponding RANGE can go from - inf ( for very, very small x) to + inf for very, very large x values

the base of the logs is irrelavent

Then for the SECOND log portion log_{6 } again you cannot have negative numbers or zero ....this means that 'x' has to be => 1 for the first log fxn (remember no negative numbers!)

then the range will change from log_{6}(1) = 0 to + infinity

so in summary domain 1<=x <= + inf

range 0 <= y <=+ inf

ElectricPavlov Jan 24, 2022