log base 2 of (x) = sqrt(x)

solve for all x values where this is true.

Question

log base 2 of (x) = sqrt(x)

solve for all x values where this is true.

jdoe0001 · Answer

$\huge log_{2}(x)=\sqrt{x}\implies 2^{\frac{x}{2}}=x$

anonymous · Answer

I actually got close to this point. What I didn't figure out was how to solve for x once you get to the equation: $$2^{\sqrt{x}} = x$$ (which is equivalent to what you solved for).

jdoe0001 · Answer

hmmm

jdoe0001 · Answer

for one yours is correct, mine isn't

jdoe0001 · Answer

$\huge log_{2}(x)=\sqrt{x}\implies 2^{x^\frac{1}{2}}=x\implies 2^{\sqrt{x}}=x$ would be correct

jdoe0001 · Answer

I can see.. offhand. that 4 works

anonymous · Answer

Really? I thought $$2^{x /2}$$ was equivalent to $$2^{x^{1/2}}$$ which is the same as $$2^{x / 2}$$ since when a power is raised to a power you just multiply. Right?

jdoe0001 · Answer

16 works too

anonymous · Answer

And yeah, i know that 4 and 16 work, but i going for how to solve these in a general sense. I tried to pick as simple of an example as I could come up with.

jdoe0001 · Answer

heheh, well  $\bf \large x^{\frac{1}{2}}\ne \frac{x}{2}$

jdoe0001 · Answer

right

anonymous · Answer

oh, derp. 

yeah.

jdoe0001 · Answer

well... hmmm there seem to be just a few values that will fit the bill for the base 2 to match up "x"

anonymous · Answer

there are only two. I know that much

jdoe0001 · Answer

well... I agree =)