Find out x if lgx = -lg2.

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

lgx=-lg2

lg x= (-1)*lg 2

    = lg (2^-1)

     = lg (1/2)

lgx= lg(1/2)

We know that if:

lg x = lg y

Then, x=y

Since lg x = lg (1/2)

==> x= 1/2

 

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

If logx = -log2,then

logx = log2^(-1). So base being the same, x = 2^(-1). Or

x = 1/2

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To find out x, first we'll have to impose constraints of existence of logarithms:

x>0

lg x=-lg 2

lg x = lg [(2)^-1]

lg x = lg 1/2

We'll use the one to one property of logarithms:

x = 1/2

Because of the fact that the solution is positive, it's convenient, so

x=1/2

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