1/2 lg(2x-1)-1 = lg0.3

First, we can simplify the equation by combining the logarithms on the left side:

lg(2x-1)^(1/2) - 1 = lg0.3

Next, we can rewrite the equation using the property of logarithms that states lg(a)^b = b * lg(a):

lg√(2x-1) - 1 = lg0.3

Now, we can remove the logarithms by exponentiating both sides with base 10:

√(2x-1) - 1 = 0.3

Next, we isolate √(2x-1) by adding 1 to both sides of the equation:

√(2x-1) = 1.3

Now, square both sides of the equation to isolate x:

2x - 1 = 1.69
2x = 2.69
x = 1.345

So, the solution to the equation is x = 1.345.