$lnx=lny$ is simplified down to?

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Answer 1 · 2018-04-20T10:12:37

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By the laws of logarithms:

$log_a(b)=log_a(c) <=>b=c$

This is obvious when you consider that if the logarithm of a number $x$ is say $b$ and you are using base $e$ logarithms, then:

$e^b=x$

If the logarithm of a number $y$ is also $b$ ( which is what the statement is saying ), and you are using the same base, then:

$e^b=y$

Since:

$e^b=e^b$

Then:

$x=y$

lnx=lnylnx=lny is simplified down to?