Question 435693
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Hi
Need to be familiar with the Properties of Logarithms

*[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) ]
In this example:
*[tex \LARGE\ \ log_2x + log_2(x+4)- log_2 7 = log_2 x(x+4)/7 = 0 ]

*[tex \LARGE\ \ \ \ \ \ \ log_2 x(x+4)/7  \ = \ 0 \ \ \Rightarrow\ \ 2^0 = x(x+4)/7]
 1 = x(x+4)/7     
  7 = x^2 + 4x
 x^2 + 4x - 7 = 0
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
    {{{x = (-4 +- sqrt(44 ))/(2) }}}
    {{{x = -2 +- sqrt(11) }}}
       x = 1.3166   |Tossing out negative solution