SOLUTION: Solve {{{3000e^(0.17x) = 4000}}} for x to four decimal places. The number e is the base of the natural logarithm function. thanks

Question 202903: Solve for x to four decimal places. The number e is the base of the natural logarithm function.
thanks
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Whenever you are asked to "Solve for x" it means: "Use Algebra to change the equation around so that "x" is isolated (by itself) on one side of the equation".

In your equation we need to use Algebra to "peel away" the 3000, the "e" and the 0.17 and we need x out of the exponent. We can deal the the 3000 easily. Just divide both sides of by 3000 giving:

which simplifies to:

In general when one has an equation of the form you use the base "a" logarithm to eliminate the "a" and to get the "x" out of the exponent at the same time. So we can deal with both the "e" and the fact that x is in an exponent by finding the ln (the base "e" logarithm) of both sides.:

Using the property on the left side we get:

Since the ln(e) = 1 we now have:

Now "x" is out of the exponent and "e" is gone! The final step is to divide both sides by 0.17:

The 0.17's on the left side cancel giving:

We have "solved for x"! It is by itself on the left side of this equation. The only thing left to do is to simplify the right side. Using our calculators to find the ln(4/3) we get:

and then dividing by 0.17:

And rounding to 4 decimal places:

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