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Popular >

simplify log_{10}(1/27)

Solution

simplify

lo g_{10} (\frac{1}{27})

Solution

- 3 lo g_{10} (3)

+1

Decimal Notation

- 1.43136 \dots

Solution steps

lo g_{10} (\frac{1}{27})

\frac{1}{27} = 2 7^{- 1}

= lo g_{10} (2 7^{- 1})

Apply log rule:

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

lo g_{10} (2 7^{- 1}) = - 1 \cdot lo g_{10} (27)

= - 1 \cdot lo g_{10} (27)

Apply rule:

1 \cdot a = a

= - lo g_{10} (27)

Factor the number:

27 = 3^{3}

= - lo g_{10} (3^{3})

Apply log rule:

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

- lo g_{10} (3^{3}) = - 3 lo g_{10} (3)

= - 3 lo g_{10} (3)

Popular Examples

factor 30n^2-19n-28 factor

30 n^{2} - 19 n - 28

simplify 2/5*1 simplify

\frac{2}{5} \cdot 1

simplify 3/5*2/4 simplify

\frac{3}{5} \cdot \frac{2}{4}

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- 6 + 0

simplify 4+4+4+4 simplify

4 + 4 + 4 + 4

Frequently Asked Questions (FAQ)

What is log_{10}(1/27) ?
The solution to log_{10}(1/27) is -3log_{10}(3)