What is 10log_{10}(0.5) ?

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

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simplify 10log_{10}(0.5)

simplify

10 lo g_{10} (0.5)

- 10 lo g_{10} (2)

Decimal Notation

- 3.01029 \dots

Solution steps

10 lo g_{10} (0.5)

0.5 = \frac{5}{10}

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

Cancel the numbers:

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

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

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

= 10 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)

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

Apply rule:

1 \cdot a = a

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

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

Apply rule:

a (- b) = - ab

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

= - 10 lo g_{10} (2)

3 x^{2} \times x

- (0)

\frac{π}{2} + 2 πn

\frac{2 x + 1}{12 x + 8} - \frac{x ^{2}}{6 x ^{2} + x - 2} + \frac{2 x}{16 x - 8}

(2) (2)