prove that the value of log₁₀2is greater than 1/4 but less than 1/3.

u can prove

3<log (base2) 10 <4 -----using the fact that log(base a) b= 1/(log (base b) a) and also that log 2(base 10) is  +ve.

as the graph of log(base a) x is increasing for a>1 so we can say that,

log 8<log 10<log 16 ------ all base 2

i.e 3< log 10<4

hence proved!! :)