the-bottom-1-2-of-log-1-2-x-wants-to-make-2-2-how-

Question Number 6877 by sarathon last updated on 01/Aug/16

the bottom (\frac{1}{2}) of {l o g}_{\frac{1}{2}} x wants to make 2

2 how ? ?

Commented by Tawakalitu. last updated on 01/Aug/16

{l o g}_{\frac{1}{2}} x

= {l o g}_{2^{- 1}} x

= - 1 {l o g}_{2}^{x}

= {l o g}_{2} x^{- 1}

= {l o g}_{2}^{\frac{1}{x}}

Answered by Rasheed Soomro last updated on 01/Aug/16

L e t {l o g}_{\frac{1}{2}} x = y

{(\frac{1}{2})}^{y} = x

{(2^{- 1})}^{y} = x

2^{- y} = x

{l o g}_{2} x = - y

y = - {l o g}_{2} x = {l o g}_{2} x^{- 1}

H e n c e {l o g}_{\frac{1}{2}} x = {l o g}_{2} (\frac{1}{x})