Solve the following for x 2 log x log2 log12 x log5 7x 3

Solve the following for x: 2 log x = log2 + log(12 - x) log_5 (7x - 3) = 2 the inequality log_7 (x + 1) + log_7, (7 - x) > 1: the equation 2 COS^2 x = 1 - cos x, for x in the interval [0, 2pi).

Solution

a. 2logx=log2 + log(12-x)

    log x²= log (2(12-x))

x²=24-2x

x²+2x-24=0

(x+6)(x-4)=0

x=-6,4

And log cant take negative values

Therefore correct answer is x=4

b. log₅(7x-3)=2

7x-3=2⁵

7x=35

x=5