What is log_{1/2}(7/12) ?

The solution to log_{1/2}(7/12) is -log_{2}(7)+2+log_{2}(3)

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simplify log_{1/2}(7/12)

simplify

lo g_{\frac{1}{2}} (\frac{7}{12})

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

Decimal Notation

0.77760 \dots

Solution steps

lo g_{\frac{1}{2}} (\frac{7}{12})

Apply log rule:

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

lo g_{\frac{1}{2}} (\frac{7}{12}) = - lo g_{2} (\frac{7}{12})

= - lo g_{2} (\frac{7}{12})

Apply log rule:

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

lo g_{2} (\frac{7}{12}) = lo g_{2} (7) - lo g_{2} (12)

= - (lo g_{2} (7) - lo g_{2} (12))

lo g_{2} (12) = 2 + lo g_{2} (3)

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

Apply the distributive law:

- (a + b) = - a - b

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

= - (lo g_{2} (7) - 2 - lo g_{2} (3))

Apply the distributive law:

- (a - b) = - a + b

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

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

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

lo g_{5} (3) + lo g_{5} (r) - lo g_{5} (w)

7 ln (x) - \frac{1}{7} ln (y)

lo g_{b} (\frac{x ^{3} y}{z ^{8}})

- \frac{1}{2} ln ∣ u ∣ + \frac{1}{2} ln ∣ u - 2 ∣

What is log_{1/2}(7/12) ?
The solution to log_{1/2}(7/12) is -log_{2}(7)+2+log_{2}(3)