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

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

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simplify log_{1/3}(2x)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= - lo g_{3} (2 x)

Apply log rule:

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

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

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

Apply the distributive law:

- (a + b) = - a - b

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

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

2 lo g_{c} (x) + 5 lo g_{c} (y) - 5 lo g_{c} (x)

\frac{1}{2} ln (10)

lo g_{a} (+ 2 lo g_{b} (x))

lo g_{10} (y^{7}) - lo g_{10} (y^{2})

- 6 \cdot lo g_{10} (11 \cdot (100 \cdot b - 72) - 8) + 6 \cdot lo g_{10} (11 \cdot b - 8)