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Popular >

simplify log_{3}(0.25)

Solution

simplify

lo g_{3} (0.25)

Solution

- 2 lo g_{3} (2)

+1

Decimal Notation

- 1.26185 \dots

Solution steps

lo g_{3} (0.25)

0.25 = \frac{25}{100}

= lo g_{3} (\frac{25}{100})

Cancel the numbers:

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

= lo g_{3} (\frac{1}{4})

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

= lo g_{3} (4^{- 1})

Apply log rule:

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

lo g_{3} (4^{- 1}) = - 1 \cdot lo g_{3} (4)

= - 1 \cdot lo g_{3} (4)

Apply rule:

1 \cdot a = a

= - lo g_{3} (4)

Factor the number:

4 = 2^{2}

= - lo g_{3} (2^{2})

Apply log rule:

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

- lo g_{3} (2^{2}) = - 2 lo g_{3} (2)

= - 2 lo g_{3} (2)

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Frequently Asked Questions (FAQ)

What is log_{3}(0.25) ?
The solution to log_{3}(0.25) is -2log_{3}(2)