Question

Solve ln (x-4) < 6

and
solve the inequality 3^2n less then or equal to 1/81

Answer 1

\[\ln(x)=y\iff e^y=x\] and since both are strictly increasing
\[\ln(x)<y\iff x<e^y\]

Answer 2

in your example
\[\ln(x-4)<6\iff x-4<e^6\]

Answer 3

what i put down as my answer before was x < e^6 +4
is that wrong?

Answer 4

you are right

Answer 5

so that answers correct? Thanks!

Answer 6

yes
as for the next one, note that \(\frac{1}{81}=3^{-4}\)

Answer 7

so is that the answer or how i would begin to solve it?

Answer 8

\[3^{2n}<3^{-4}\iff 2n<-4\iff n<-2\]

Answer 9

I'm a bit confused, so the answer would be n <-2 ?

Answer 10

Are you still there?

Answer 11

yes, that is the answer

Answer 12

Thanks for all of your help!