Solve for x ? 2lg x=lg(3x-2)

First, we'll use the power property of logarithms for the left term:

2lg x = lg(x^2)

We'll re-write the equation:

lg(x^2) = lg(3x-2)

We'll use the one to one property:

x^2 = 3x-2

We'll move all termsto the left side:

x^2 - 3x + 2 = 0

We'll use the quadratic formula:

x1 = [3+sqrt(9-8)]/2

x1 = (3+1)/2

x1 = 2

x2 = 1

We'll verify the results into equation:

2lg x1=lg(3x1 - 2)

2lg2 = lg(6-2)

lg 2^2 = lg4

lg4 = lg4

2lg x2=lg(3x2 - 2)

2lg 1=lg(3-2)

2*0 = lg 1

0 = 0

So, both values of x are the solutions of the equation:

x1 = 2 and x2 = 1