Solve the exponential equation. Express the solution as an exact answer in terms of natural logarithms

Question

𝑒9−5𝑥=6981

I got the decimal approximation of the answer but I have to enter the log version into webwork as well and because it is so specific about how the answer must be formatted I cannot seem to enter it in correctly as hard as I try.

the natural log answer I came up with (which worked for the decimal approximation) is (ln(6981)-9)/5 but webwork says this is incorrect.

Answer 1

As far as I can tell, you just about got it but may have made a very minor algebra mistake. Assuming the problem is written as follows (the exponent is not entirely clear the way it has been typed above, but I am making an assumption):

e^(9-5x) = 6981, (take the natural log of both sides)

9 - 5x = ln(6981), (subtract 9 from each side)

-5x = ln(6981) - 9, (divide by negative 5, this is where I see the mistake)

x = -[ln(6981) - 9] / 5

Did this fix it? It looks like you understood the concept but maybe just made a minor calculation error.