What is log_{1/2}(7/(x^2)) ?

The solution to log_{1/2}(7/(x^2)) is -log_{2}(7)+2log_{2}(x)

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simplify log_{1/2}(7/(x^2))

simplify

lo g_{\frac{1}{2}} (\frac{7}{x ^{2}})

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

Solution steps

lo g_{\frac{1}{2}} (\frac{7}{x ^{2}})

Apply log rule:

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

lo g_{\frac{1}{2}} (\frac{7}{x ^{2}}) = - lo g_{2} (\frac{7}{x ^{2}})

= - lo g_{2} (\frac{7}{x ^{2}})

Apply log rule:

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

lo g_{2} (\frac{7}{x ^{2}}) = lo g_{2} (7) - lo g_{2} (x^{2})

= - (lo g_{2} (7) - lo g_{2} (x^{2}))

Simplify

lo g_{2} (x^{2}) : 2 lo g_{2} (x)

= - (lo g_{2} (7) - 2 lo g_{2} (x))

Apply the distributive law:

- (a - b) = - a + b

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

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

lo g_{10} (x y) + lo g_{10} (\frac{y}{x})

ln (14) - ln (2)

- lo g_{10} (1.2 \cdot 1 0^{- 4})

lo g_{3} (z) + lo g_{3} (z + 2)

ln (\frac{e ^{2}}{3})

What is log_{1/2}(7/(x^2)) ?
The solution to log_{1/2}(7/(x^2)) is -log_{2}(7)+2log_{2}(x)