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gledanju0

gledanju0

Answered question

2022-06-26

Proving log x 2 = 2 log x
How does log x 2 = 2 log x
Can you do a proof please. I know that this is true but I don't know why.

Answer & Explanation

scipionhi

scipionhi

Beginner2022-06-27Added 25 answers

Apply the exponential to get:
e log ( x 2 ) = x 2 = ( e log ( x ) ) 2 = e log ( x ) e log ( x ) = e 2 log ( x )
Averi Mitchell

Averi Mitchell

Beginner2022-06-28Added 8 answers

Assuming you have the following understaning of what is a logarithm:
x = log b a a = b x
So, let we have the following values:
x = log b a and y = log b c
Which means that:
a = b x and y = log b c
If we multiply a and c:
a c = b x b y = b x + y
Hence, by our definition of logarithm:
x + y = log b ( a c ) = log b a + log b c (do you remember that x and y are the logarithms of a and b?)
So, we have prooved that:
log b ( a c ) = log b a + log b c
Now just use that formula in your particular case to get:
log b ( x 2 ) = log b ( x x ) = log ( x ) + log ( x ) = 2 log ( x )

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