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

Question

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

shane_b · Answer

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

anonymous · Answer

yes that is the problem

shane_b · Answer

$$37=550e^{-.2x}$$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:$$x=\frac{ln(\frac{37}{550})}{-.2}$$

anonymous · Answer

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

anonymous · Answer

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

shane_b · Answer

np