Question

Solve for x using logarithms. Give an exact answer. Do not give a decimal approximation.
37 = 550e−0.2x

Answer 1

First, is this the problem?\[\large 37=550e^{-.2x}\]

Answer 2

yes that is the problem

Answer 3

\[37=550e^{-.2x}\]First divide both sides by 550 to get:\[\frac{37}{550}=e^{-.2x}\]Then take the natural log of both sides:\[ln(\frac{37}{550})=ln(e^{-.2x})\]\[ln(\frac{37}{550})=(-.2x)lne\]
lne=1 so that becomes:
\[ln(\frac{37}{550})=-.2x\]Finally, divide both sides by -.2 to isolate x:\[x=\frac{ln(\frac{37}{550})}{-.2}\]

Answer 4

that's what I put originally and it was marked wrong

Answer 5

wait, just kidding. I put -0.02 in the denominator the first time..thanks

Answer 6

np