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

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) (Show Source): You can put this solution on YOUR website!

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:

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 is equivalent to . Using this on our equation we get:

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 ). Either way you should get something close to 0.3678794411714423 which, rounded to the nearest thousandth, is 0.368.
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