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

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The discussion focuses on simplifying logarithmic expressions, specifically the equation log2(41/2) = 1. Participants clarify that 2^1 equals 4^1/2, leading to confusion about the logarithmic relationships. It is confirmed that log4(2) equals 1/2, while log2(2) equals 1. The equivalence of logarithmic forms is emphasized, illustrating how different bases yield consistent results. Understanding these relationships is crucial for simplifying logarithmic expressions effectively.
lionely
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Write in log form

2= 41/2I wrote this log2 41/2 = 1?

But looking at what I wrote doesn't make sense...
 
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Why it doesn't make sense to you? :confused:
 
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
 
lionely said:
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. loga(x)= y is equivalent to ay= x. Taking the logarithm, base 4, of both sides of 2= 41/2 gives log4(2)= log4(41/2)= 1/2. But taking the logarithm, base 2, gives log2(2)= 1= log2(41/2)= log2((22)1/2)= log2(21)= 1.
 

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