When proving the product, quotient, or power rule of logarithms, various properties of logarithms and exponents must be used.
Which property listed below is used in all of these proofs?

the relations are:

Ln(a*b) = ln(a) + ln(b)

ln(a/b) = ln(a) - ln(b)

a*ln(b) = ln(b^a)

the relation used is:

1)  exp(a)*exp(b) = exp(a+b)

and remember that exp(x) = y

means that ln(y) = x

then when we apply logaritm to both sides in the equation 1) we must have that:

ln( exp(a)*exp(b)) = ln(exp( a+b)) = a+ b

ln( exp(a)*exp(b)) = a + b

then

ln( exp(a)*exp(b)) = ln(exp(a)) + ln(exp(b)) = a + b

and you can use a similar thinking to prove the other ones, using that relationships and:

exp(a - b) = exp(a)/exp(b)

exp(a)^b = exp(a*b)

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