What is log_{1/3}(x)+log_{1/3}(x+2) ?

The solution to log_{1/3}(x)+log_{1/3}(x+2) is -log_{3}(x(x+2))

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simplify log_{1/3}(x)+log_{1/3}(x+2)

simplify

lo g_{\frac{1}{3}} (x) + lo g_{\frac{1}{3}} (x + 2)

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

Solution steps

lo g_{\frac{1}{3}} (x) + lo g_{\frac{1}{3}} (x + 2)

Apply log rule:

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

lo g_{\frac{1}{3}} (x) + lo g_{\frac{1}{3}} (x + 2) = lo g_{\frac{1}{3}} (x (x + 2))

= lo g_{\frac{1}{3}} (x (x + 2))

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

lo g_{\frac{1}{3}} (x (x + 2)) = - lo g_{3} (x (x + 2))

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

ln (x^{8} - 1) - ln (x^{3} - 1)

lo g_{x} (7 b)

lo g_{4} (16 (x^{2} - 49))

lo g_{10} (ab c)

ln (- 5 x)

What is log_{1/3}(x)+log_{1/3}(x+2) ?
The solution to log_{1/3}(x)+log_{1/3}(x+2) is -log_{3}(x(x+2))