I need 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.