Simplify this:please?

Question

e^ln3

e^(1+lnx)

ln1

lne^7 will this be 7lne?

Answer 1

1)

In general, e^(ln(x)) = x.  Remember that ln(x) means "What power do I need to raise e to, in order to get back x?"  So the first answer is 3.

2)

Remember that (a^b)(a^c) = a^(b+c), so use this in reverse to get

e * e^(lnx) = e x

3)

Remember that x^0 = 1, so log(1) = 0 whatever base you're using.  

4)

Yes, but you can simplify it further.  Again, ln(x) means  "What power do I need to raise e to, in order to get back x?"  So ln(e) = 1.  This gives you a final answer of 7.