SOLUTION: Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this. 3 ln x = -3 Can you help? Thank you!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this. 3 ln x = -3 Can you help? Thank you!      Log On


   

Question 250811: Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.
3 ln x = -3
Can you help? Thank you!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
3ln%28x%29+=+-3
With the variable in the argument of a logarithm like this, you often start the solution by transforming the equation into one of the following forms:
log(expression) = other-expression
or
log(expression) = log(other-expression)

Our equation is pretty close to the first form. All we have to is eliminate the 3 in front of the logarithm by dividing both sides by 3:
ln%28x%29+=+-1
We now have the first form. The next step with this form is to rewrite the equation in exponential form. To do this we have to remember that log%28a%2C+%28p%29%29+=+q is equivalent to p+=+a%5Eq. Using this on our equation we get:
x+=+e%5E%28-1%29
This is an exact expression for the answer. To get a decimal approximation we can use 2.7182818284590451 (or a rounded off version of it) for e and use our calculators to raise it to the -1 power. (If you don't know how to raise to a negative power, then just divide 1 by e (since e%5E%28-1%29+=+1%2Fe). Either way you should get something close to 0.3678794411714423 which, rounded to the nearest thousandth, is 0.368.