Proving log ⁡ x 2 = 2 log ⁡ xHow does log ⁡ x 2...

gledanju0

gledanju0

Answered

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

Expert

2022-06-27Added 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

Expert

2022-06-28Added 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 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?