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Popular >

simplify log_{125}(1/5)

Solution

simplify

lo g_{125} (\frac{1}{5})

Solution

- \frac{1}{3}

+1

Decimal Notation

- 0.33333 \dots

Solution steps

lo g_{125} (\frac{1}{5})

Factor the number:

125 = 5^{3}

= lo g_{5^{3}} (\frac{1}{5})

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{5^{3}} (\frac{1}{5}) = \frac{1}{3} lo g_{5} (\frac{1}{5})

= \frac{1}{3} lo g_{5} (\frac{1}{5})

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

= \frac{1}{3} lo g_{5} (5^{- 1})

Apply log rule:

lo g_{a} (a^{b}) = b

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

= \frac{1}{3} (- 1)

\frac{1}{3} (- 1) = - \frac{1}{3}

= - \frac{1}{3}

Popular Examples

200(x+5)=250-50x

200 (x + 5) = 250 - 50 x

2 ∣ x - 5 ∣ > 32

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x^{4} - 2 x^{3} - 4 x^{2} + 18 x - 45

factor 625x^4-16y^4 factor

625 x^{4} - 16 y^{4}

simplify 2/9*3 simplify

\frac{2}{9} \cdot 3

Frequently Asked Questions (FAQ)

What is log_{125}(1/5) ?
The solution to log_{125}(1/5) is -1/3