Log2 x = logx 2

Question

Logbase2 of x = logbasex of 2

 

 

Answer 1

There could be another answer also.

That is,

y=-1

x^(-1)=2

x=1/2

Answer 2

log(2)x=log(x)2

let log(2)x=y and let log(x)2=y because they are equal to each other

log(2)x=y means 2^y=x

log(x)2=y means x^y=2

substituting, (x^y)^y=x

x^y²=x, y²=1, y=1

log(2)x=1, 2¹=x, x=2

log(x)2=1, x¹=2, x=2

log(2)2=log(2)2