Let log base 4 of 3 = x. Then log base 8 of 27 = kx. Find k.
k =2
log 4 3 = x log 8 27 = kx
Put these in exponential form
4x = 3 8kx = 27
(22)x = 3 (23)kx = 27
(22x) = 3 (22x) 1.5k = 27
(3)1.5k = 27
(3)1.5k = 33
Solve for the exponents
1.5k = 3
k = 2
Flip 'em to base 10 log 3/ log 4 = x
log 27 /log8 = kx = k log3/log4
k = log27/log8 * log4/log3 = 2