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anonymous
 one year ago
Solve for x using the natural logarithm:
anonymous
 one year ago
Solve for x using the natural logarithm:

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jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.0kinda hard to do, when the expression is invisible

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[2\times4^{x} = 9.5e ^{2x}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you for your patience, @jdoe0001

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@SithsAndGiggles Can you help?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.0hmmm can you pot a quick screenshot of the material?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@zepdrix Can you help? I'm desperate :(

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm 2\cdot4^{x} = 9.5\cdot e ^{2x}\]I don't like decimals, fractions are better, so I'm gonna do something a little sneaky. Let's umm.... let's multiply both sides by 2, then divide each side by 4,\[\large\rm 4^x=\frac{19}{4}e^{2x}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Then take natural log each side I guess, ya? :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \ln\left(4^x\right)=\ln\left(\frac{19}{4}e^{2x}\right)\]We have to apply a bunch of fun log rules to solve for x.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \color{orangered}{\log(a^b)=b\cdot \log(a)}\]Do you see how this orange rule might help us on the left side of our equation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait why doesn't 4 cancel out when you divide it?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Umm if that was too confusing, we can just do it this way instead :)\[\large\rm 2\cdot4^{x} = 9.5\cdot e ^{2x}\]Dividing by 2 gives us:\[\large\rm 4^{x} = 4.75\cdot e ^{2x}\]I just didn't like the decimal value, so I changed it to a fraction, but we can leave it like this if it's easier to understand.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So taking log of each side gives us\[\large\rm \ln\left(4^x\right)=\ln\left(4.75\cdot e^{2x}\right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So you get x(ln4) = ln(4.75e^2x) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And now ln and e cancel each other out

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Left side looks good. Woops! Don't try to cancel out the e just yet! Gotta do some more simplifying before you can do that.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \color{orangered}{x\ln4}=\ln\left(4.75\cdot e^{2x}\right)\]How bout the right side? How can we apply this blue rule?\[\large\rm \color{royalblue}{\log(a\cdot b)=\log(a)+\log(b)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x(ln4)= ln(4.75) + ln(e^2x) ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ok great! Now we don't have the number in front of the e, so we can "cancel" them out like you wanted.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm x \ln4=\ln4.75+\ln e^{2x}\]\[\large\rm x \ln4=\ln4.752x\]mmmm k good!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Let's get all of our x's to one side and try some factoring.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x(ln4) + 2x= ln4.75 ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1cool :) the terms on the left side both have something in common. try to factor it out :O

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x(ln4 + 2)= ln4.75 ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Good good good, how you gonna wrap it up? :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Yayyy good job \c:/ If your teacher wants you to leave it as an exact value you would have:\[\large\rm x=\frac{\ln4.75}{2+\ln4}\] But yes, that's a correct decimal approximation.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yay!!! You are the BEST!!! Thanks so much!
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