What is log_{1/2}(3/10) ?

The solution to log_{1/2}(3/10) is -log_{2}(3)+1+log_{2}(5)

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simplify log_{1/2}(3/10)

simplify

lo g_{\frac{1}{2}} (\frac{3}{10})

- lo g_{2} (3) + 1 + lo g_{2} (5)

Decimal Notation

1.73696 \dots

Solution steps

lo g_{\frac{1}{2}} (\frac{3}{10})

Apply log rule:

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

lo g_{\frac{1}{2}} (\frac{3}{10}) = - lo g_{2} (\frac{3}{10})

= - lo g_{2} (\frac{3}{10})

Apply log rule:

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

lo g_{2} (\frac{3}{10}) = lo g_{2} (3) - lo g_{2} (10)

= - (lo g_{2} (3) - lo g_{2} (10))

lo g_{2} (10) = 1 + lo g_{2} (5)

= - (lo g_{2} (3) - (1 + lo g_{2} (5)))

Apply the distributive law:

- (a + b) = - a - b

- (1 + lo g_{2} (5)) = - 1 - lo g_{2} (5)

= - (lo g_{2} (3) - 1 - lo g_{2} (5))

Apply the distributive law:

- (a - b) = - a + b

- (lo g_{2} (3) - 1 - lo g_{2} (5)) = - lo g_{2} (3) + 1 + lo g_{2} (5)

= - lo g_{2} (3) + 1 + lo g_{2} (5)

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

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

3.8 + lo g_{10} (\frac{0.19}{0.41})

lo g_{10} (\frac{y}{100})

ln (\frac{1}{2 x ^{3}})

What is log_{1/2}(3/10) ?
The solution to log_{1/2}(3/10) is -log_{2}(3)+1+log_{2}(5)