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trupinoyboi
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find the exact solution, using common logarithms, and a twodecimalplace approximation of the solution 4^x3(4^x)=8
 10 months ago
 10 months ago
trupinoyboi Group Title
find the exact solution, using common logarithms, and a twodecimalplace approximation of the solution 4^x3(4^x)=8
 10 months ago
 10 months ago

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agent0smith Group TitleBest 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.
 10 months ago

trupinoyboi Group TitleBest ResponseYou've already chosen the best response.0
im terribly confused as to how i would apply common logarithms to this problem. :(
 10 months ago

Mertsj Group TitleBest ResponseYou've already chosen the best response.2
You 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.
 10 months ago

trupinoyboi Group TitleBest ResponseYou've already chosen the best response.0
dw:1386036292570:dw i ended up with this
 10 months ago

trupinoyboi Group TitleBest ResponseYou've already chosen the best response.0
dw:1386036395791:dw would it turn to this?
 10 months ago

agent0smith Group TitleBest ResponseYou've already chosen the best response.1
Can'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.
 10 months ago

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

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

agent0smith Group TitleBest ResponseYou've already chosen the best response.1
Check your math in the quadratic formula, looks like your numbers aren't right.
 10 months ago

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

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

Mertsj Group TitleBest ResponseYou've already chosen the best response.2
Divide both sides by log 4
 10 months ago

trupinoyboi Group TitleBest ResponseYou've already chosen the best response.0
I am so grateful to both of you. Thank you so much! :)
 10 months ago
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