Question 451125
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Hi
*[tex \LARGE\ \ log_5(c-2) + log_5(c+4) = log_5(c-2)(c+4) = 5 ]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ log_b(x) \ = \ y \ \ \Rightarrow\ \ b^y = x]
  (c-2)(c+4) = 5^5
  c^2 +2c - 8 = 3125
  c^2 + 2c - 3133 = 0 
{{{c = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{c = (-2 +- sqrt( 12536))/(2) }}}
Solutions: 54.9821, -56.9821 (note: negative solution is Extraneous)
   c = 54.9821
Important to be familiar with the following:
*[tex \large \ \ \ \ \ \ \ \ \ \ log_b(x) \ = \ y \ \ \Rightarrow\ \ b^y = x]
*[tex \large\ \ nlog_bx = log_b(x^n) ]
*[tex \large\ \ log_bx + log_by = log_b(xy) ]
*[tex \large\ \ log_bx - log_by = log_b(x/y) ]