Question 818289
log5(3x+7) + log5(x-5)= 2

<pre>
{{{log (5, (3x + 7)) + log (5, (x - 5))= 2}}}
{{{log (5, (3x + 7)(x - 5)) = 2}}}
{{{(3x + 7)(x - 5) = 5^2}}}
{{{3x^2 - 8x - 35 = 25}}}
{{{3x^2 - 8x - 60 = 0}}}
(3x + 10){x - 6) = 0
3x = - 10             OR        x = 0 + 6
{{{x = - 10/3}}}               OR        {{{x = 6}}}
Since {{{- 10/3}}} will yield the log of a negative number, so ignore this solution. Thus, the only solution is: {{{highlight_green(x = 6)}}}
You can do the check!!

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