Question 5352
Combine logarithms on the left side using the law of logarithms: {{{ln a + ln b = ln (ab) }}}


ln(7-x)+ln(3x+5)=ln(24x)
ln (7-x)(3x+5) = ln(24x)


Raise both sides as a power of e to "undo" the lns:

(7-x)(3x + 5) = 24x
{{{21x + 35 - 3x^2 - 5x - 24x = 0}}}
{{{-8x - 3x^2 +35 = 0}}}


Multiply both sides by -1, and write in descending powers of x:
{{{3x^2 + 8x - 35 = 0}}}, which just happens to factor!! (Imagine that!!)
{{{(3x- 7)(x+5) = 0 }}}
{{{x= 7/3}}} {{{x= -5}}}


You are not allowed to have a log of a negative in the real numbers, so you must reject the -5.  The final answer is {{{x= 7/3}}}.


R^2 at SCC