Question

`lnx=lny` is simplified down to?

Answer 1

`color(blue)(x=y)`

Explanation:

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`