document.write( "Question 401048: Solve
\n" ); document.write( "3ln(y +4) = 2 ln(x +2) − 2ln(x +9)+ 3ln(x^2 − 1).\r
\n" ); document.write( "\n" ); document.write( "i ) Determine the range of values of x and y for which the expressions on
\n" ); document.write( "each side of this equation are defined\r
\n" ); document.write( "\n" ); document.write( "ii ) Find y explicitly as a function of x, that is, express the equation in the
\n" ); document.write( "form y = f(x), simplifying your answer as far as possible. \n" ); document.write( "
Algebra.Com's Answer #283964 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
Solve
\n" ); document.write( "3ln(y +4) = 2 ln(x +2) − 2ln(x +9)+ 3ln(x^2 − 1).
\n" ); document.write( "i ) Determine the range of values of x and y for which the expressions on
\n" ); document.write( "each side of this equation are defined
\n" ); document.write( "ii ) Find y explicitly as a function of x, that is, express the equation in the
\n" ); document.write( "form y = f(x), simplifying your answer as far as possible.\r
\n" ); document.write( "\n" ); document.write( "(i)For logx, x>0
\n" ); document.write( "3ln(y +4) = 2 ln(x +2) − 2ln(x +9)+ 3ln(x^2 − 1)
\n" ); document.write( "range & domain as follows:
\n" ); document.write( "y+4>0
\n" ); document.write( "y>-4 (-4,infinity)
\n" ); document.write( "x+2>0
\n" ); document.write( "x>-2 (-2,infinity)
\n" ); document.write( "x+9>0
\n" ); document.write( "x>-9 (not in domain)
\n" ); document.write( "x^2-1>0
\n" ); document.write( "x^2>1
\n" ); document.write( "x>1 or x<-1 (-infinity,-1)union(1,infinity)\r
\n" ); document.write( "\n" ); document.write( "Simplifying equation:
\n" ); document.write( "3ln(y +4) = 2 ln(x +2) − 2ln(x +9)+ 3ln(x^2 − 1)
\n" ); document.write( "ln(y+4)^3=ln(x+2)^2-ln(x+9)^2+ln(x^2-1)^3
\n" ); document.write( "0=ln(x+2)^2+ln(x^2-1)^3-ln(x+9)^2-ln(y+4)^3
\n" ); document.write( "0=ln(x+2)^2+ln(x^2-1)^3-(ln(x+9)^2+ln(y+4)^3)
\n" ); document.write( "0=ln((x+2)^2)*((x^2-1)^3)/((x+9)^2)*((y+4)^3)
\n" ); document.write( "e^0=(x+2)^2)*((x^2-1)^3)/((x+9)^2)*((y+4)^3)
\n" ); document.write( "1=(x+2)^2)*((x^2-1)^3)/((x+9)^2)*((y+4)^3)
\n" ); document.write( "(y+4)^3=(x+2)^2)*((x^2-1)^3)/((x+9)^2)
\n" ); document.write( "taking the cube root of each side
\n" ); document.write( "y+4=((x+2)^2/3)*(x^2-1)/((x+9)^2/3))
\n" ); document.write( "y=((x+2)^2/3)*(x^2-1)/((x+9)^2/3))-4
\n" ); document.write( "f(x)={((x+2)^2/3)*(x^2-1)/((x+9)^2/3)}-4
\n" ); document.write( " \n" ); document.write( "
\n" );