lnx-ln3=2

Question

lnx-ln3=2

mathstudent55 · Answer

Here's a rule of logs:

$\ln(ab) = \ln a - \ln b$

mathstudent55 · Answer

$ \ln x- \ln 3 = 2 $

$\ln \dfrac{x}{3} = 2 $

Now use the definition of log.

mathstudent55 · Answer

Definition of log:

$\log_b x = y$ means $b^y = x$

anonymous · Answer

is says here use one to one property to solve for x?

mathstudent55 · Answer

What is one to one property?

anonymous · Answer

if loga(m) = loga(n) then m=n

mathstudent55 · Answer

Here there is log only on the left side. The right side is simply 2.

anonymous · Answer

then x = 5?

mathstudent55 · Answer

No. Are you sure the problem up on top is the correct problem?
Was it supposed to be 
ln x - ln 3 = ln 2 ?
Did you leave out the ln with the 2 on the right side?

anonymous · Answer

yep the problem is correct, my bad it says solve log. ew. algebriacally

anonymous · Answer

*log. eq.

mathstudent55 · Answer

If the problem is correct, then let's continue where we left off.
We need to use the definition of log to continue.
Remember that ln is log base e.

mathstudent55 · Answer

We were here:

$\ln \dfrac{x}{3} = 2$

This means the same as:

$\log_e \dfrac{x}{3} = 2$

Using the definition, we get:

$e^2 = \dfrac{x}{3} $

Now multiply both sides by 3.

anonymous · Answer

x=3e^2??

mathstudent55 · Answer

Correct.