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anonymous
 one year ago
Solve 4^(2x) = 7^(x−1).
anonymous
 one year ago
Solve 4^(2x) = 7^(x−1).

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Astrophysics @rishavraj @ganeshie8

freckles
 one year ago
Best ResponseYou've already chosen the best response.2have you tried taking ln( ) of both sides

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\ln(4^{2x})=\ln(7^{x1}) \\ \\ \text{ Now use power rule } \\ 2x \ln(4)=(x1) \ln(7)\] you can use log too if you want

freckles
 one year ago
Best ResponseYou've already chosen the best response.2not distribute on the right hand side

freckles
 one year ago
Best ResponseYou've already chosen the best response.2and put your terms with x in it on one side and your terms without x on the opposing side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01.38629436112(2x) I mean, sorry :)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2are you allowed to approximate ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no, not until we have the final answer

freckles
 one year ago
Best ResponseYou've already chosen the best response.2ok so leave that one side as 2ln(4)x and distribute on the other side recall the distributive property is a(b+c)=ab+ac

freckles
 one year ago
Best ResponseYou've already chosen the best response.2use distributive property here and what do you get: \[\ln(7)(x1)=?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01.94591014906x1.94591014906

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I think you mean to say ln(7)xln(7)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\ln(4^{2x})=\ln(7^{x1}) \\ \\ \text{ Now use power rule } \\ 2x \ln(4)=(x1) \ln(7) \\ 2 \ln(4) x=\ln(7) x \ln(7) \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2now to get the x people together subtract ln(7)x on both sides

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[ax=bxc \\ axbx=c \\ x(ab)=c \\ \text{ the last step is to choose to divide by } \\ \text{ what is in front of the } x \\ \\ \text{ in this example that would be } (ab) \\ x=\frac{c}{ab}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2this is exactly what you are going to do here first subtract ln(7)x on both sides then use my example as a guide sorta to finally find x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.02.77258872224x=1.94591014906x1.94591014906

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I thought you aren't allowed to approximate until you have final answer

freckles
 one year ago
Best ResponseYou've already chosen the best response.2ln(7) is irrational there is no way you can write out the whole number same for ln(4)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh. Sorry, I just typed it into my calculator & thats what it said

freckles
 one year ago
Best ResponseYou've already chosen the best response.2your calculator can only show you so many digits

freckles
 one year ago
Best ResponseYou've already chosen the best response.2it doesn't have an infinite screen display

freckles
 one year ago
Best ResponseYou've already chosen the best response.2anyways... \[\ln(4^{2x})=\ln(7^{x1}) \\ \\ \text{ Now use power rule } \\ 2x \ln(4)=(x1) \ln(7) \\ 2 \ln(4) x=\ln(7) x \ln(7) \\ \text{ the step I was asking you \to do is subtract } \ln(7) x \text{ on both sides } \\ 2 \ln(4) x \ln(7) x=\ln(7)\] try factoring the x out on the left hand side like I did in my example axbx=x(ab)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.02 In(x)In(3)x=In (7)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2dw:1438798478614:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\ln(4^{2x})=\ln(7^{x1}) \\ \\ \text{ Now use power rule } \\ 2x \ln(4)=(x1) \ln(7) \\ 2 \ln(4) x=\ln(7) x \ln(7) \\ \text{ the step I was asking you \to do is subtract } \ln(7) x \text{ on both sides } \\ 2 \ln(4) x \ln(7) x=\ln(7) \\ ( 2 \ln(4)\ln(7) )x=\ln(7)\] I'm going to leave the last step to you

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright, so I got 2 In (3) =In(7) In(3)^2=In(7) yes?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.02.35389<is my answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I gotta go eat lunch:) Please message me if I was wrong

freckles
 one year ago
Best ResponseYou've already chosen the best response.2not sure where you got 2 ln(3)=ln(7) just divide both sides by what x is being multiplied by which is 2ln(4)ln(7) this does not equal 2 ln(3) divide both sides by 2ln(4)ln(7)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\ln(4^{2x})=\ln(7^{x1}) \\ \\ \text{ Now use power rule } \\ 2x \ln(4)=(x1) \ln(7) \\ 2 \ln(4) x=\ln(7) x \ln(7) \\ \text{ the step I was asking you \to do is subtract } \ln(7) x \text{ on both sides } \\ 2 \ln(4) x \ln(7) x=\ln(7) \\ ( 2 \ln(4)\ln(7) )x=\ln(7) \\ x=\frac{\ln(7)}{2 \ln(4)\ln(7)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2http://www.wolframalpha.com/input/?i=ln%287%29%2F%282ln%284%29ln%287%29%29 this calculator says that is approximately 2.35
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