Determine lg x lg 2SolutionFirst of all we have to set the

Determine lg x = - lg 2

Solution

First of all, we have to set the existence conditions:

x>0

The interval of admissible values for x is (0,+inf.)

We\'ll use the power property of logarithm:

lg x=-lg 2

lg x = lg 2^-1

We\'ll use the property of negative exponent:

a^-x = 1/a^x, so 2^-1 = 1/2

lg x = lg 1/2

Because the bases are matching, we\'ll use the one to one property of logarithms:

x=1/2>0

Since the value belongs to the interval of admissible values, we\'ll accept the root of the equation x = 1/2.