Question 134410
Given : log(7x^2+30x+2) - 2log(x+1) = 1

Use the values on both side and raise 10 to that number

{{{10^(log(7x^2+30x+2) - 2log(x+1)) = 10^1}}}
{{{(10^(log(7x^2+30x+2)))/(10^(2log(x+1))) = 10}}}
{{{(7x^2+30x+2)/((x+1)^2) = 10}}}
{{{(7x^2+30x+2)= 10(x+1)^2}}}
{{{7x^2+30x+2 = 10x^2 + 20x + 10}}}
{{{0 = 3x^2 -10x + 8}}}

Use the quadratic equation
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
Find x = 2, x = 8/6

Check by subbing back into the original equation and using your calculator