Expanding Logarithms with Radicals

[Deagonx]

Homework Statement

log₂√x

Homework Equations

The Attempt at a Solution

I thought that it might be something like log₂x - log₂x but that's not right. The book examples don't have any radicals.

 

[Mark44]

Homework Statement

log₂√x

Homework Equations

The Attempt at a Solution

I thought that it might be something like log₂x - log₂x but that's not right. The book examples don't have any radicals.

Write √x with a fractional exponent.

 

[Deagonx]

That makes a lot more sense... So is it 1/2(log₂x) or (log₂x)/2(log₂x)

 

[scurty]

That makes a lot more sense... So is it 1/2(log₂x) or (log₂x)/2(log₂x)

$log(a^b) = b \cdot log(a)$

 

[HallsofIvy]

That makes a lot more sense... So is it 1/2(log₂x) or (log₂x)/2(log₂x)

Why would you even consider that $log_2(\sqrt{x})= 1/2$ for all x?