Question 250811
{{{3ln(x) = -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)<br>
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(x) = -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(a, (p)) = q}}} is equivalent to {{{p = a^q}}}. Using this on our equation we get:
{{{x = e^(-1)}}}
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^(-1) = 1/e}}}). Either way you should get something close to 0.3678794411714423 which, rounded to the nearest thousandth, is 0.368.