What is log_{10}(2*10^{-2}) ?

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

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simplify log_{10}(2*10^{-2})

simplify

lo g_{10} (2 \cdot 1 0^{- 2})

lo g_{10} (2) - 2

Decimal Notation

- 1.69897 \dots

Solution steps

lo g_{10} (2 \cdot 1 0^{- 2})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (2 \cdot 1 0^{- 2}) = lo g_{10} (2) + lo g_{10} (1 0^{- 2})

= lo g_{10} (2) + lo g_{10} (1 0^{- 2})

Apply log rule:

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

lo g_{10} (1 0^{- 2}) = - 2 lo g_{10} (10)

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

2 lo g_{10} (10) = 2

= lo g_{10} (2) - 2

ln (\frac{∣ 8 + 2 x ∣}{∣ - 2 + 2 x ∣})

2 (2 ln ∣ x + 2 ∣ - ln ∣ x + 1 ∣)

- \frac{1}{0.024} ln (\frac{6 - p}{4.2})

\frac{19 ln ( \frac{y}{x} + 5 ) - ln ( \frac{y}{x} )}{5} - \frac{y}{x}

ln (\frac{x}{\frac{x}{2}})

What is log_{10}(2*10^{-2}) ?
The solution to log_{10}(2*10^{-2}) is log_{10}(2)-2