can anyone help me simplify this problem? ln(x-3)(x+2)-ln(x+2)^2-ln7
ln(x-3)(x+2) - ln(x+2)^2 - ln7
= ln [ (x-3)(x+2)/( 7(x+2)^2 )
= ln (x-3)/( 7(x+2) )
thank you very much
Of course! I'd be happy to help you simplify the given problem.
First, let's start by expanding the expression:
ln(x-3) + ln(x+2) - ln(x+2)^2 - ln(7)
Next, we can combine the two ln terms by subtracting the exponents:
ln[(x-3)(x+2)/(x+2)^2] - ln(7)
Now, let's simplify the expression inside the ln:
ln[(x^2-x-6)/(x^2+4x+4)] - ln(7)
To further simplify, we can combine the two ln terms into a single ln expression:
ln[(x^2-x-6)/(x^2+4x+4*7)]
Since 4*7 equals 28, we can simplify the expression even further:
ln[(x^2-x-6)/(x^2+4x+28)]
And that is the simplified form of the given expression.