Question

how would you solve t ln(t)- t > 0?

Answer 1

t>0,because t is in the In()

Answer 2

start with \(t(\ln(t)-1)>0\)

Answer 3

I simplified that to ln t>1...is that correct?

Answer 4

that is not really "simpler" if you want to solve this inequality

Answer 5

t > e^1

Answer 6

you have
\[t(\ln(t)-1)>0\] and we know that the domain of the log is \(t>0\) so the first factor is always positive
then it comes down to solving
\[\ln(t)-1>0\implies \ln(t)>1\implies t>e\]

Answer 7

oh i am sorry i did not read your answer carefully
yes, it comes down to \(\ln(t)>1\) as you said