What is log_{1/2}(1/2000) ?

The solution to log_{1/2}(1/2000) is log_{2}(2000)

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simplify log_{1/2}(1/2000)

simplify

lo g_{\frac{1}{2}} (\frac{1}{2000})

lo g_{2} (2000)

Decimal Notation

10.96578 \dots

Solution steps

lo g_{\frac{1}{2}} (\frac{1}{2000})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{\frac{1}{2}} (\frac{1}{2000}) = lo g_{\frac{1}{2}} (1) - lo g_{\frac{1}{2}} (2000)

= lo g_{\frac{1}{2}} (1) - lo g_{\frac{1}{2}} (2000)

Apply log rule:

lo g_{a} (1) = 0

= 0 - lo g_{\frac{1}{2}} (2000)

0 - lo g_{\frac{1}{2}} (2000) = - lo g_{\frac{1}{2}} (2000)

= - lo g_{\frac{1}{2}} (2000)

Apply log rule:

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

= - (- lo g_{2} (2000))

Apply rule

- (- a) = a

= lo g_{2} (2000)

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