Question

$prove \: that \: {2}^{ log_{2} } = 1$
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Answer 1

To Prove :

2ˡᵒᵍ²= 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Property of log

=>Logₑa = 1

=>(logm)^n = nlogm

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=>2ˡᵒᵍ²= 1

let us assume the the equation equal to y

let y = 2ˡᵒᵍ²

Now,apply log base 2 to both sides

=>log₂y = log₂ 2ˡᵒᵍ²

=>2ˡᵒᵍ² is in the form of (logm)^n

So,it becomes 2log₂

=>log₂y=log₂log₂2

Log base a of a will always equal to 1

=>log₂y=log₂

=>log₂ is on the same side ( as also Logₑa = 1 )

=>log₂y=log₂

=>y= 1

So, y = 1 (proved)

Extra information=>

=>logm × logn => logm+logn

=>logm ÷ logn=logm -logn

=>logₐx²=logₐx × logₐx = 2log x