if logb2x and logb3y evaluate the following in terms of x an

if logb(2)=x and logb(3)=y, evaluate the following in terms of x and y: (a) logb 108 (b) logb 24 (c) logb 8/3 (d) (logb 9)/(logb 8) Thanks.

a) logb(108)

108 = 4*27 = 4*3^3 = 2^2*3^3

logb(2^2*3^3) = logb2^2 +logb3^3 = 2logb(2) +3logb(3) = 2x +3y

b) logb(24)

24 = 3*2^3

So, logb(24) = logb(3*2^4) = logb(3) +logb(2^4) = y +4x

c) logb(8/3) = logb8 - logb3

= lob2^3 -logb3 = 3logb2 -logb3 = 3x -y

d) logb(9)/logb(8) = logb(3^2)/logb(2^3) = 2logb(3)/3logb(2)

= 2y/3x