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

The solution to log_{1/2}(1/10) is log_{2}(10)

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

simplify

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

lo g_{2} (10)

Decimal Notation

3.32192 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - lo g_{\frac{1}{2}} (10)

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

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

Apply log rule:

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

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

Apply rule

- (- a) = a

= lo g_{2} (10)

lo g_{9} (5) e^{3} + lo g_{9} (7) e^{6}

- lo g_{10} (3.98 \cdot 1 0^{- 3})

ln (2 e^{t a n (x)})

ln (e^{x} - 1) - ln (x)

ln (\frac{1}{a} e^{5 a})