Verified answer

if

a^(3/2) * a^(-2) * 3√a = a^b

is your equation then here's how to solve:

take the ln of both sides

ln(a^(3/2) * a^(-2) * 3√a) = ln(a^b)

now you can bring down the exponent

ln(a^(3/2) * a^(-2) * 3√a) = b*ln(a)

b = ln(a^(3/2) * a^(-2) * 3a^(1/2)) / ln(a)

Now combine exponents. All the a's in the top ln cancel out.

b = ln(3) / ln(a)

Hope this helps.