Question

Which of the following is equivalent to log9 36 ?

Answer 1

9=3^2 36=4*9=2^2*3^2
\[\log_{9} 36=\log_{3^2} (4*9)=\log_{3^2}4 +\log_{3^2} 9=\log_{3^2} 2^2+\log_{3^2} 3^2=\log_{3} 2+1\]

Answer 2

because \[\log_{x^a} y^b=(b/a)\log_{x} y\]