Proof of logarithmic identity log_g x=log_a x*log_g a I know that this can be written as: (ln x)/(ln g}=(ln x)/(ln g) But does this prove the alleged link or do i have to do something further?

Elsa Brewer

Elsa Brewer

Answered question

2022-07-21

Proof of logarithmic identity log g x = log a x log g a
I have to prove the alleged link between the logarithms in base g and a
log g x = log a x log g a
I know that this can be written as:
ln x ln g = ln x ln g
But does this prove the alleged link or do i have to do something further?
I know that this is derived from:
log g x = ln x ln g

Answer & Explanation

penangrl

penangrl

Beginner2022-07-22Added 17 answers

Using your last formula ( log g ( x ) = ln ( x ) ln ( g ) )
log g ( x ) log a ( x ) = ln ( x ) ln ( g ) ln ( x ) ln ( a ) = ln ( x ) ln ( a ) ln ( x ) ln ( g ) = ln ( a ) ln ( g ) = log g ( a ) log g ( x ) = log g ( a ) log a ( x ) .
Q.E.D.
Tirimwb

Tirimwb

Beginner2022-07-23Added 2 answers

g log a x × log g a = ( g log g a ) log a x = a log a x = x = g log g x
hence:
log a x × log g a = log g x

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