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# algebra

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70
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Solve 4^x + 2^x + 1 = 111.

Dec 4, 2020

#1
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so first we can simplify $4^x$ into $2^2x$. So $2^2x$+$2^x$+$1$=$111$, next is $2^2x$+$2^x$=$110$, add so that it is \$2^3x=110, take log on both sides and you get 2.260453

pls check if I am correct and don't submit answer until verify

Dec 4, 2020
#2
+31533
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Let $$u = 2^x$$, then we have $$u^2+u+1=111$$, or $$u^2 + u - 110 = 0$$ or $$(u - 10)(u + 11) = 0$$

Assuming ony a real number solution for x means we want u = 10 and $$x=\frac{\ln(10)}{\ln(2)}$$

Dec 5, 2020