What is log_{3}(8)+log_{3}(x)-2log_{3}(x+4) ?

The solution to log_{3}(8)+log_{3}(x)-2log_{3}(x+4) is log_{3}((8x)/((x+4)^2))

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simplify log_{3}(8)+log_{3}(x)-2log_{3}(x+4)

simplify

lo g_{3} (8) + lo g_{3} (x) - 2 lo g_{3} (x + 4)

lo g_{3} (\frac{8 x}{( x + 4 ) ^{2}})

Solution steps

lo g_{3} (8) + lo g_{3} (x) - 2 lo g_{3} (x + 4)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{3} (8) + lo g_{3} (x) = lo g_{3} (8 x)

= lo g_{3} (8 x) - 2 lo g_{3} (x + 4)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 lo g_{3} (x + 4) = lo g_{3} ((x + 4)^{2})

= lo g_{3} (8 x) - lo g_{3} ((x + 4)^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{3} (8 x) - lo g_{3} ((x + 4)^{2}) = lo g_{3} (\frac{8 x}{( x + 4 ) ^{2}})

= lo g_{3} (\frac{8 x}{( x + 4 ) ^{2}})

2 ln (x) + \frac{1}{2} ln (x^{2} - 1) - \frac{1}{2} ln (x^{2} + 1)

ln (\frac{11}{3})

ln (\frac{e}{a})

ln (\frac{p}{1 - p})

ln (\frac{60}{70})

What is log_{3}(8)+log_{3}(x)-2log_{3}(x+4) ?
The solution to log_{3}(8)+log_{3}(x)-2log_{3}(x+4) is log_{3}((8x)/((x+4)^2))