What is log_{5}(x-2)+log_{5}(3x+7) ?

The solution to log_{5}(x-2)+log_{5}(3x+7) is log_{5}((x-2)(3x+7))

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simplify log_{5}(x-2)+log_{5}(3x+7)

simplify

lo g_{5} (x - 2) + lo g_{5} (3 x + 7)

lo g_{5} ((x - 2) (3 x + 7))

Solution steps

lo g_{5} (x - 2) + lo g_{5} (3 x + 7)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{5} (x - 2) + lo g_{5} (3 x + 7) = lo g_{5} ((x - 2) (3 x + 7))

= lo g_{5} ((x - 2) (3 x + 7))

\frac{1}{2} ln (x + 3) - ln (x)

ln (9 e^{x})

2 (lo g_{6} (x) + 2 lo g_{6} (y) - 3 lo g_{6} (z))

\frac{1}{3} (3 ln (x + 4) + ln (x) - ln (x^{2} - 5))

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

What is log_{5}(x-2)+log_{5}(3x+7) ?
The solution to log_{5}(x-2)+log_{5}(3x+7) is log_{5}((x-2)(3x+7))