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

If log_b2=x and log_b3=y, evaluate the following in terms of x and y

(a)logb144                (c) logb 8/3

(b) logb6                   (d) logb27/logb2           *all the b\'s are supposed to be like how they are in the Q

Solution

we have x = log_b 2 and y = log_b 3.

(a) log_b 144 = log_b (2⁴ * 3²) = log_b 2⁴ + log_b 3² = 4log_b 2 + 2log_b 3 = 4x + 3y

(b) log_b 6 = log_b 2 * 3 = log_b 2 + log_b 3 = x + y

(c) log_b (8/3) = log_b 8 - log_b 3 = log_b 2³ - log_b 3 = 3log_b 2 - log_b 3 = 3x - y

(d) log_b 27/ log_b 2 = log_b 3³ / log_b 2 = 3log_b 3 / log_b 2 = 3y/x