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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{\frac{1}{2}} (4 a^{3}) = lo g_{\frac{1}{2}} (4) + lo g_{\frac{1}{2}} (a^{3})

= lo g_{\frac{1}{2}} (4) + lo g_{\frac{1}{2}} (a^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{\frac{1}{2}} (a^{3}) = 3 lo g_{\frac{1}{2}} (a)

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

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

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

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

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

ln ∣ p ∣ - ln ∣ d ∣

ln (5) - ln (2) - \frac{21}{50}

ln (b t e^{- d t})

ln (∣ x ∣^{2}) + 2 ln ∣ x ∣

x + ln (x) + 5 - ln (2)