What is log_{1/2}(1/5) ?

The solution to log_{1/2}(1/5) is log_{2}(5)

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simplify log_{1/2}(1/5)

simplify

lo g_{\frac{1}{2}} (\frac{1}{5})

lo g_{2} (5)

Decimal Notation

2.32192 \dots

Solution steps

lo g_{\frac{1}{2}} (\frac{1}{5})

Apply log rule:

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

lo g_{\frac{1}{2}} (\frac{1}{5}) = - lo g_{2} (\frac{1}{5})

= - lo g_{2} (\frac{1}{5})

\frac{1}{5} = 5^{- 1}

= - lo g_{2} (5^{- 1})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{2} (5^{- 1}) = - 1 \cdot lo g_{2} (5)

= - (- 1 \cdot lo g_{2} (5))

Apply rule:

1 \cdot a = a

- 1 \cdot lo g_{2} (5) = - lo g_{2} (5)

= - (- lo g_{2} (5))

Apply rule:

- (- a) = a

- (- lo g_{2} (5)) = lo g_{2} (5)

= lo g_{2} (5)

lo g_{3} (9^{2} \cdot 7^{4})

3 x^{2} + 51 x + 216

\frac{1}{3} \cdot \frac{3}{4}

25 \cdot 1 0^{- 3}

\frac{3 x + 9}{x ^{2} - 9}