Question 363142
{{{ln(3x-1)=ln(5)-ln(x-5)}}}
{{{ln(3x-1)=ln(5/(x-5))}}}
{{{3x-1=5/(x-5)}}}
{{{(3x-1)(x-5)=5}}}
{{{3x^2-15x-x+5=5}}}
{{{3x^2-16x=0}}}
{{{x(3x-16)=0}}}
Two solutions:
{{{highlight(x=0)}}}
.
.
.
{{{3x-16=0}}}
{{{3x=16}}}
{{{highlight(x=16/3)}}}
.
.
.
However, since {{{x=0}}} would lead to a negative argument for the natural log function it is not allowed as a solution.
{{{highlight_green(x=16/3)}}}