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 1/3<(log)_(10)3<1/2dot

Prove that 2/5 lt log_(10) 3 lt 1/2 .

Prove that (tan3x)/(tanx) never lies between 1/3a n d3 .

Prove that log_3log_2log_(sqrt3) 81=1

Prove that (tan x)/(tan 3 x) never lies between 1/3 and 3.

Prove that for real values of x ,(a x^2+3x-4)//(3x-4x^2+a) may have any value provided a lies between 1 and 7.

(i) If log(a + 1) = log(4a - 3) - log 3, find a. (ii) If 2 log y - log x - 3 = 0, express x in termss of y. (iii) Prove that : log_(10) 125 = 3(1 - log_(10)2) .

Prove that log(1+2+3)=log1+log2+log3

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