Question

Find the exact value of x if 8^x = "i'll show you below"

Answer 1

\[8^x = \sqrt{2\sqrt{8\sqrt{2}}}\]

Complicated, i know, but if you can solve it WITHOUT using a calculator, pls show working, thanks :P

Answer 2

\[8^{x}=\sqrt{2\sqrt{8(2)^{1/2}}}\]
\[8^{x}=\sqrt{2\sqrt{2^{3}(2)^{1/2}}}\]
\[8^{x}=\sqrt{2\sqrt{2^{3}(2)^{1/2}}}\]
\[8^{x}=\sqrt{2\sqrt{(2)^{7/2}}}\]
\[8^{x}=\sqrt{2((2)^{7/2})^{1/2}}\]
\[8^{x}=\sqrt{2((2)^{7/4})}\]
\[8^{x}=\sqrt{((2)^{11/4})}\]
\[2^{3x}=((2)^{11/4})^{1/2}\]
\[2^{3x}=((2)^{11/8})\]
3x=11/8
x=11/24

Answer 3

HOLY MOTHER OF GOD OMFG THATS RIGHT YOU, ARE AWESOME :P
sorry, i've been dying over that question for days, and my teacher was refusing to tell me how to do it :P Thanks :)

Answer 4

LOL