Question 200476
Applying log rules:
{{{ log ( 3, ( x- 2) ) + log (3, ( x- 4) ) = 2 }}}
{{{ log ( 3, ( x- 2)( x- 4) ) = 2 }}}
{{{ ( x- 2)( x- 4) = 3^2 }}}
{{{ x^2- 4x -2x +8 = 9 }}}
{{{ x^2- 6x +8 = 9 }}}
{{{ x^2- 6x - 1 = 0 }}}
Solving for x using the quadratic equation yields:
x = {6.162, -0.162}
We can throw out the negative solution leaving:
x = 6.162
.
Details of quadratic follows:
*[invoke quadratic "x", 1, -6, -1 ]