What is log_{10}(0.25) ?

The solution to log_{10}(0.25) is -2log_{10}(2)

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simplify log_{10}(0.25)

simplify

lo g_{10} (0.25)

- 2 lo g_{10} (2)

Decimal Notation

- 0.60205 \dots

Solution steps

lo g_{10} (0.25)

0.25 = \frac{25}{100}

= lo g_{10} (\frac{25}{100})

Cancel the numbers:

\frac{25}{100} = \frac{1}{4}

= lo g_{10} (\frac{1}{4})

\frac{1}{4} = 4^{- 1}

= lo g_{10} (4^{- 1})

Apply log rule:

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

lo g_{10} (4^{- 1}) = - 1 \cdot lo g_{10} (4)

= - 1 \cdot lo g_{10} (4)

Apply rule:

1 \cdot a = a

= - lo g_{10} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

= - 2 lo g_{10} (2)

\frac{7 x}{x y + 7 x + 7} + \frac{y}{yz + y + 7} + \frac{z}{x z + z + 1}

- 4^{- 1}

(7 + 2 i) - (- 3 - 3 i)

\frac{x + 2}{x ^{2} - 3 x - 18} - \frac{5 x}{x - 6}

lo g_{0} (x)