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trupinoyboi
 2 years ago
find the exact solution, using common logarithms, and a twodecimalplace approximation of the solution 4^x3(4^x)=8
trupinoyboi
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0im terribly confused as to how i would apply common logarithms to this problem. :(

Mertsj
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1386036292570:dw i ended up with this

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

agent0smith
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0I ended up with \[4^x= \frac{ 8+\sqrt{52} }{ 2 }\]

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

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

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

trupinoyboi
 2 years 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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