log(x+8)-log(2)=log(2x+2) solution set
To find the solution set for the equation log(x+8) - log(2) = log(2x+2), we can use logarithmic properties and algebraic techniques.
First, let's simplify the equation using logarithmic properties. The subtraction of logs is equivalent to the division of their arguments, so we have:
log[(x+8)/2] = log(2x+2)
Now, to solve for x, we need to eliminate the logarithms. This can be done by equating the arguments of the two logarithms:
(x+8)/2 = 2x + 2
Next, we can multiply both sides of the equation by 2 to eliminate the fraction:
x + 8 = 4x + 4
Simplifying further:
3x = 4
Finally, divide both sides of the equation by 3 to solve for x:
x = 4/3
Therefore, the solution to the equation log(x+8) - log(2) = log(2x+2) is x = 4/3.