<img src="https://tex.z-dn.net/?f=%20%7Bx%20%7D%5E%7B2%7D%20%3D%20%20%7B16%7D%5E%7Bx%3F%7D%20%20%20" id="TexFormula1" title=" {x

mariarad [96]

3 years ago

}^{2} = {16}^{x?} " alt=" {x }^{2} = {16}^{x?} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

lora16 [44]3 years ago

5 0

X is -1/2 . Using the Lambert W function.
x^2=16^x => x^2=(2^4)^x
x^2=2^4x => x=2^2x
x=(e^in(2))^2x => x=e^2in(2)x
e^2in(2)x1/x=1
xe^-2in(2)x=1 /*1
-xe^-2in(2)x=-1
-2in(2)xe^-2in(2)x=-2in(2)
W(-2in(2)xe^-2in2x)=W(-2in(2))
-2in(2)x=W(-2in(2))
X=-W(-2in(2))/2in(2)

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