" 15.(i) "log_(a)x

Evaluate each of the following in terms of x and y, if it is given x=log_(2)3 and y=log_(2) 5. (i) log_(2)15

Find x, if : (i) log_(x) 625 = -4 (ii) log_(x) (5x - 6) = 2 .

Find x, if : (i) log_(2) x = -2 (ii) log_(4) (x + 3) = 2 (iii) log_(x) 64 = (3)/(2)

Solve : (i) x^(log_(10)x)= 100x .

Find x, if : (i) log_(10) (x + 5) = 1 (ii) log_(10) (x + 1) + log_(10) (x - 1) = log_(10) 11 + 2 log_(10) 3

Given 2 log_(10) x + 1 = log_(10) 250 , find : (i) x (ii) log_(10) 2x

Differentiate the following function with respect to x (i) log_(x)x(ii)e^(3log x)

State, true or false : (i) If log_(10)x = a , then 10^(x) = a (ii) If x^(y) = z , then y = log_(z) x . (iii) log_(2) 8 = 3 and log_(8) 2 = (1)/(3) .

Find x, if : (i) log_(3) x = 0 (ii) log_(x) 2 = -1 (iii) log_(9) 243 = x (iv) log_(5) (x - 7) = 1 (v) log_(4) 32 = x - 4 (vi) log_(7) (2x^(2) - 1) = 2

Solve (i) log_(0.2) |x-3|ge0 (ii) log_(0.5) ((3-x)/(x+2))lt0