What is log_{1/3}(1/6) ?

The solution to log_{1/3}(1/6) is log_{3}(6)

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simplify log_{1/3}(1/6)

simplify

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

lo g_{3} (6)

Decimal Notation

1.63092 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - lo g_{\frac{1}{3}} (6)

0 - lo g_{\frac{1}{3}} (6) = - lo g_{\frac{1}{3}} (6)

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

Apply log rule:

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

= - (- lo g_{3} (6))

Apply rule

- (- a) = a

= lo g_{3} (6)

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

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

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\frac{1}{- 0.06437} ln (\frac{1}{20})

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