If logx 5 32 then x 23 32 1125 125 none of these If loga 2x

If log_x 5= 3/2 then x= 2/3 3/2 1/125 125 none of these If log_a 2=x and log_a 3=y then log_a 12= x+2y x-2y 2x-y 2x+y 2xy For a > 0 and b > 0, log a/b= log a/log b log a+ log b log a - log b log b - log a b log a

Solution

Q. 2 If log_x 5 = 3/2 , then 5 = x^3/2 so that 5^2/3 = (x^3/2)^2/3 = x^3/2*2/3 = x. Thus, x =5^2/3. The 1^st option is the correct answer.

Q. 7 If log_a2 = x , then log_a 4 = log_a 2² = 2log_a 2 = 2x. Also, log_a 3 = y, so that log_a12 = log_a 4*3 = log_a 4+ log_a 3 = 2x+y. Thus, log_a12 = 2x+y ( as log mⁿ = n log m and log (mn) = log m +log n).The 4^th option is the correct answer.

Q. 4 For a > 0 and b > 0, log (a/b) = log a – log b ( by the properties of logarithmic operations).The 3^rd option is the correct answer.