Ineed to rewrite this as an exponential equation
lnx=9
i also need to rewrite this as a logarithmic equation
e4 =y
i'm not quite sure where to start.

Step-by-step explanation:

The trick is knowing the link between logarithmic functions and exponential functions.  

if you have an exponential function like this b^x = a you can turn it into a logarithmic function log_b(a) = x.  You say it log base b of a equals x.  As you can tell this form is useful for solving for the exponent if it is a variable.  I'll give an example.

2^x = 8

I made it easy, you could just try a few values for x and you'd be able to tell x = 3  THis also means log_2(8) = 3

One more thing to mention, if the "base" number is e that is a special kind of log called the natural log, which you can write as ln(x).  so basically ln(x) = log_e(x) (log base e of x).

Now, we can deal with your problems.

ln(x) = 9  Remember ln is log base e

log_e(x) = 9 And also remember log_b(a)=x can be written as b^x=a

e^9 = x

e^4 = y is just that in reverse.

log_e(y) = 4

ln(y) = 4

If you ever get it in the form log_e your teachers are going to want you to convert it to ln, so keep that in mind to.  

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>

8

step-by-step explanation:

just put √(2) * √(32) into a calculator. that will make the answer be 8.