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 one year ago
find the exact solution, using common logarithms, and a twodecimalplace approximation of the solution 4^x3(4^x)=8
 one year ago
find the exact solution, using common logarithms, and a twodecimalplace approximation of the solution 4^x3(4^x)=8

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agent0smith
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large 4^x3(4^{x})=8\]first subtract 8 on both sides \[\Large 4^x3(4^{x})8=0\]I would multiply both sides by 4^x \[\Large 4^{2x}38(4^x) = 0\](think about exponent laws and you'll see how to get it. Now it's like a quadratic.

trupinoyboi
 one year ago
Best ResponseYou've already chosen the best response.0im terribly confused as to how i would apply common logarithms to this problem. :(

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.2You could say: Let 4^x=y then you would have : y^28y3=0 Solve for y using the quadratic formula. Set each answer equal to 4^x and take the log of both sides.

trupinoyboi
 one year ago
Best ResponseYou've already chosen the best response.0dw:1386036292570:dw i ended up with this

trupinoyboi
 one year ago
Best ResponseYou've already chosen the best response.0dw:1386036395791:dw would it turn to this?

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.1Can't read that. \[\Large 4^{2x}38(4^x) = 0\]if you understand to here, do as merts said. Let y = 4^x \[\Large y^2 8y  3 = 0\]solve using quadratic formula.

trupinoyboi
 one year ago
Best ResponseYou've already chosen the best response.0I ended up with \[4^x= \frac{ 8+\sqrt{52} }{ 2 }\]

trupinoyboi
 one year ago
Best ResponseYou've already chosen the best response.0The answer i should end up with\[\frac{ \log(4+\sqrt{19)} }{\log4 }\]

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.1Check your math in the quadratic formula, looks like your numbers aren't right.

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.2\[y=\frac{8\pm \sqrt{644(1)(3)}}{2}=\frac{8\pm \sqrt{76}}{2}=\frac{8\pm2\sqrt{19}}{2}=4\pm \sqrt{19}\]

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.2\[4^x=4+\sqrt{19}\] \[x \log_{10}4=\log_{10}(4+\sqrt{19}) \]

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.2Divide both sides by log 4

trupinoyboi
 one year ago
Best ResponseYou've already chosen the best response.0I am so grateful to both of you. Thank you so much! :)
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