Prove that `log_(10)`2lies between `1/3` and `1/4`.

Prove that log_(10) 2" lies between " 1/4 and 1/3 .

Prove that log_(3) 81- 4 =0

Prove that 5costheta+3cos(theta+pi/3)+3 lies between -4 and 10.

If sin theta= 21/29 , prove that sec theta+ tan theta= 2 1/2 if theta lies between 0 and pi//2 .

Prove that (log_(2)8)/(log_(3)9) =3/2

The value of log_(10)3 lies in the interval

If xsqrt(1+y) + ysqrt(1+x) = 0 for x lies between -1 and 1 prove that dy/dx =-1/(1+x)^2

Prove that log_n(n+1)>log_(n+1)(n+2) for any natural number n > 1.

Find the equation of plane passing through the points : (2, - 1, 1), B (4, 3, 2) and C (6, 5, -2). Also, prove. that the point (5, -1,-2:) lies on the plane given by A, B and C.

Prove that following: underset(1)overset(3)int(dx)/(x^2(x+1))=2/3 + log(2)/(3)