What is 20log_{10}(0.5) ?

The solution to 20log_{10}(0.5) is -20log_{10}(2)

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simplify 20log_{10}(0.5)

simplify

20 lo g_{10} (0.5)

- 20 lo g_{10} (2)

Solution steps

20 lo g_{10} (0.5)

0.5 = \frac{5}{10}

= 20 lo g_{10} (\frac{5}{10})

Cancel the numbers:

\frac{5}{10} = \frac{1}{2}

= 20 lo g_{10} (\frac{1}{2})

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

= 20 lo g_{10} (2^{- 1})

Apply log rule:

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

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

= 20 (- 1 \cdot lo g_{10} (2))

Apply rule:

1 \cdot a = a

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

= 20 (- lo g_{10} (2))

Apply rule:

a (- b) = - ab

20 (- lo g_{10} (2)) = - 20 lo g_{10} (2)

= - 20 lo g_{10} (2)

(n + 1)^{3} + (n - 1)^{3}

20 lo g_{10} (100)

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