What is log_{1/2}(3/4) ?

The solution to log_{1/2}(3/4) is -log_{2}(3)+2

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simplify log_{1/2}(3/4)

simplify

lo g_{\frac{1}{2}} (\frac{3}{4})

- lo g_{2} (3) + 2

Decimal Notation

0.41503 \dots

Solution steps

lo g_{\frac{1}{2}} (\frac{3}{4})

Apply log rule:

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

lo g_{\frac{1}{2}} (\frac{3}{4}) = - lo g_{2} (\frac{3}{4})

= - lo g_{2} (\frac{3}{4})

Apply log rule:

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

lo g_{2} (\frac{3}{4}) = lo g_{2} (3) - lo g_{2} (4)

= - (lo g_{2} (3) - lo g_{2} (4))

lo g_{2} (4) = 2

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

Apply the distributive law:

- (a - b) = - a + b

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

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

4 lo g_{10} (3) + lo g_{10} (2)

lo g_{10} (x^{3}) - lo g_{10} (y^{2})

\frac{1}{3} ln (x - 3) - 4 ln (z) + ln (y + 7)

lo g_{10} ((\frac{p ^{4}}{q ^{7}})^{2})

- lo g_{10} (2.6 \cdot 1 0^{- 4})