NEED HELP ASAP let logb(2)=A and logb(3)=C. write logb(8)+logb(sqrt2/27) in terms of a and c

Question

log_b(2)=A, log_b(3)=C

log_b(8)+log_b(√2/27)

the √2/27 is from top to bottom. meaning the square root is all together with the fraction.

Answer 1

log_b(2^3)+log_b((2/27)^1/2)=

3log_b(2)+1/2(log_b(2/27))=

3A+1/2(log_b(2)-log_b(27))=

3A+1/2(A-log_b(3^3))=

3A+1/2(A-3log_b(3))=

3A+1/2(A-3C)