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

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

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simplify log_{1/2}(2e^3)

simplify

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

- 1 - 3 lo g_{2} (e)

Decimal Notation

- 5.32808 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

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

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

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

\frac{0.01 \cdot 2415}{π \cdot 0.003 \cdot 51271} \cdot ln (\frac{10}{60})

lo g_{\frac{1}{3}} (\frac{1}{6})

ln (y - 2) - \frac{1}{3} ln (y - 1)

3 ln (4) - ln (\frac{4}{3})