Log2 of 41/2 = 1: Simplifying Logarithms in Simple Steps

[lionely]

Write in log form

2= 4^1/2I wrote this log₂ 4^1/2 = 1?

But looking at what I wrote doesn't make sense...

 

[Saitama]

Why it doesn't make sense to you?

 

[lionely]

oh wow I'm sorry I just noticed it...
2^1= does equal 4^1/2 = 2 ... I was confused because in the back of the book I saw log4 2= 1/2

 

[HallsofIvy]

oh wow I'm sorry I just noticed it...
2^1= does equal 4^1/2 = 2 ... I was confused because in the back of the book I saw log4 2= 1/2

Yes that's also true. log_a(x)= y is equivalent to a^y= x. Taking the logarithm, base 4, of both sides of 2= 4^1/2 gives log₄(2)= log₄(4^1/2)= 1/2. But taking the logarithm, base 2, gives log₂(2)= 1= log₂(4^1/2)= log₂((2²)^1/2)= log₂(2¹)= 1.