$$\left({\left({\frac{\left({\sqrt{{\mathtt{2}}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\sqrt{{\mathtt{2}}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}\right)}^{{log8}{\left({\mathtt{0.25}}\right)}}\right) = {{\mathtt{1}}}^{{{log}}_{{\mathtt{8}}}{\left({\mathtt{0.25}}\right)}}$$

$${{\mathtt{2}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}{\mathtt{\,-\,}}{{\mathtt{4}}}^{{\mathtt{x}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{8}}}^{{\mathtt{x}}} = {\mathtt{0}}$$

Can anyone tell me what are the steps for this ?

And how i can solve the second one ?

Guest Nov 19, 2014

#2**+10 **

$$\\2^{(x-2)}-4^x+8^x=0\\

2^x*2^{-2}-2^{2x}+2^{3x}=0\\

2^x*2^{-2}-(2^{x})^2+(2^{x})^3=0\\

2^x(2^{-2}-2^{x}+(2^{x})^2)=0\\

2^x \mbox{ cannot equal zero so}\\

2^{-2}-2^{x}+(2^{x})^2=0\\

$Let $ y=2^x\\

2^{-2}-y+y^2=0\\

y^2-y+\frac{1}{4}=0\\\\

y=\frac{1\pm\sqrt{1-1}}{2}=\frac{1}{2}\\

$therefore$\\

\frac{1}{2}=2^x\\

2^{-1}=2^x\\

x=-1$$

Melody Nov 20, 2014

#1**+5 **

For the top equation: there is: (√2 - 1) / (√2 - 1) ---> but this equals 1. So any finite exponent of 1 will work.

For the second equation:

2^(x - 2) - 4^x + 8^x = 0

---> 2^(x - 2) - (2^2)^x + (2^3)^x = 0

---> 2^(x - 2) - 2^(2x) + 2^(3x) = 0 ---> x = -1 (I solved it by graphing; but it checks fairly easily.)

geno3141 Nov 19, 2014

#2**+10 **

Best Answer

$$\\2^{(x-2)}-4^x+8^x=0\\

2^x*2^{-2}-2^{2x}+2^{3x}=0\\

2^x*2^{-2}-(2^{x})^2+(2^{x})^3=0\\

2^x(2^{-2}-2^{x}+(2^{x})^2)=0\\

2^x \mbox{ cannot equal zero so}\\

2^{-2}-2^{x}+(2^{x})^2=0\\

$Let $ y=2^x\\

2^{-2}-y+y^2=0\\

y^2-y+\frac{1}{4}=0\\\\

y=\frac{1\pm\sqrt{1-1}}{2}=\frac{1}{2}\\

$therefore$\\

\frac{1}{2}=2^x\\

2^{-1}=2^x\\

x=-1$$

Melody Nov 20, 2014