Question 4895
{{{ log((6x+5)/3)=log (2/x)}}}


If log M = log N, then M = N, so
{{{ (6x+5)/3 = 2/x}}}


Multiply both sides by the common denominator which is 3x:
{{{(3x)*(6x+5) /3 = (3x)*2/x }}}
{{{x*(6x+5)  = 3*2 }}}

{{{6x^2 + 5x = 6}}}

{{{6x^2 + 5x - 6 = 0}}}

{{{ (3x - 2)(2x + 3) = 0}}}

{{{x = 2/3 }}} {{{x = -3/2}}}

The second solution is not allowed since the log of negative is not allowed in the real number system.


Final answer:  {{{x=2/3}}}

R^2 at SCC