Solve for x using logarithms. Give an exact answer. Do not give a decimal approximation.

53 = 350e^−0.4x

Question

Solve for x using logarithms. Give an exact answer. Do not give a decimal approximation.

53 = 350e^−0.4x

jdoe0001 · Answer

$\bf \large 53 = 350e^{−0.4x} \quad ?$

anonymous · Answer

yes

jdoe0001 · Answer

$\bf 53 = 350e^{−0.4x} \implies \cfrac{50}{350}= e^{−0.4x}\
\textit{recall the log cancellation rule of } log_aa^x = x\
log_e\left(\cfrac{50}{350}\right) = log_e\left(e^{−0.4x}\right)$


what would that equate to?

jdoe0001 · Answer

notice  that $\bf \textit{log cancellation rule of } log_\color{red}{a}\color{red}{a}^x = x\

log_e\left(\cfrac{50}{350}\right) = log_\color{red}{e}\left(\color{red}{e}^{−0.4x}\right)$

jhonyy9 · Answer

@jdoe0001 ATTENTION !!!

the first term is 53 and not 50  !!!