Question 1184275
Please help me solve this equation
if log(x^3+3)base 10 - log(x+7)base 10 + log2base10= log x base10, find the value of x
<pre>It's the NORM to apply base 10 for LOGS without a base, so we have: {{{matrix(1,3, log ((x^3 + 3)) - log ((x + 7)) + log ((2)), "=", log ((x)))}}}

          Since all logs above have the same base, we can say that: {{{matrix(2,3, log (((x^3 + 3))/(x + 7)) * 2, "=", log ((x)), log (2(x^3 + 3)/(x + 7)), "=", log ((x)))}}}

      With logs having same base on both sides of equation, we get: {{{matrix(1,3, 2(x^3 + 3)/(x + 7), "=", x)}}}
                                                                    {{{matrix(3,3, 2(x^3 + 3), "=", x(x + 7), 2x^3 + 6, "=", x^2 + 7x, 2x^3 - x^2 - 7x + 6, "=", 0)}}} -------- Cross-multiplying
Using the RATIONAL ROOT THEOREM, we find 2 of the 3 roots. x = 1, and x = - 2. When long division of polynomials or
SYNTHETIC DIVISION is used, we find the other root to be {{{3/2}}}.
Therefore, {{{highlight_green(matrix(3,3, x, "=", 1, x, "=", - 2, x, "=", 3/2))}}}

Thanks to IKLEYN for pointing this out. I failed to notice that one of the solutions is negative and therefore creates 
an EXTRANEOUS solution, Therefore, correct solutions are: {{{highlight_green(matrix(2,3, x, "=", 1, x, "=", 3/2))}}}.
Thanks, @IKLEYN.</pre>