Log laws proof using only rational exponents For all real a>0 and rational b>0, Show that ln(a^b)=b ln(a)

Celeste Barajas

Celeste Barajas

Answered question

2022-11-02

Log laws proof using only rational exponents
For all real a > 0 and rational b > 0
Show that ln ( a b ) = b ln ( a )

Answer & Explanation

martinmommy26nv8

martinmommy26nv8

Beginner2022-11-03Added 16 answers

b ln a = b 1 a 1 x d x = 1 a b x d x
Let u = x b
Then d u = b x b 1 d x and d u u = b x d x
Therefore, 1 a b x d x = 1 a b d u u = ln a b

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