Question

The value of log2√3 1728=

Answer 1

I will assume you meant 2√3 to be the base, that is, you want log<sub)2√3</sub> 1728

let x = log<sub)2√3</sub> 1728
(2√3)^x = 1728
2√3 = 1728^(1/x)
square both sides
12 = 1728^(2/x) , but 12^3 = 1728
12 = 12^(6/x)
so 6/x = 1
x = 6

This is probably not the easiest way to do it, but I just followed the flow

Answer 2

Since 2√3 = √12, you have
log_{_√12}12^3
= 3log_{_√12}12
= 3*2
= 6