Solve for x showing steps: 27e^[x^(3)+4] = e^7

Question

anonymous · Answer

http://www.wolframalpha.com/input/?i=27e%5E%5Bx%5E%283%29%2B4%5D+%3D+e%5E7&dataset=

helder_edwin · Answer

take natural logarithms on both sides

anonymous · Answer

ln27e^[x^(3)+4] = lne^7
I understand that the exponents are dropped down, but what happens to the 27 in front of the e?

helder_edwin · Answer

$$\large \ln(AB)=\ln A+\ln B$$
u have
$$\large 27e^{x^3+4}=e^7 $$
from this
$$\large \ln(27e^{x^3+4})=\ln e^7 $$

anonymous · Answer

divide by $27$ first

anonymous · Answer

$$x^3+4=\ln(\frac{e^7}{27})$$

isaiah.feynman · Answer

Alternatively, divide both sides by 27. you get $$e^{x^{3}+4}=\frac{ e^{7} }{ 27}$$Take natural logs of both sides$$x^{3}+4=\ln \left( \frac{ e^{7} }{ 27 } \right)$$Using logarithm rules on the right side we have$$x^{3}+4=\ln e^{7}-\ln27$$The right side simplifies to $$x^{3}+4=7-\ln27$$ You can now solve for x from here.

anonymous · Answer

then you can write $$\ln(e^7)-\ln(27)=7-\ln(27)$$

anonymous · Answer

and don't forget $3-\ln(27)$ is just some number, so you can solve via taking the cubed root

anonymous · Answer

Thank you guys so much!