Help with logarithms

Question

64 - ^3a =4²

Answer 1

For this type of problem, you'll want to find a common base. You have 4 on the right-hand side, so let's see if we can change the 64 on the left-hand side. Conveniently, 64 = 4³. So, replace 64 with 4³:

 

(4³)^-3a = 4²

 

Multiply the exponents on the left-hand side:

 

4^-9a = 4²

 

Take the log₄ of both sides and simplify, since log_n(n^m) = m:

 

log₄(4^-9a) = log₄(4²)

-9a = 2

a = -2/9