What is log_{10}(2)+log_{10}(0.2) ?

The solution to log_{10}(2)+log_{10}(0.2) is log_{10}(2/5)

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simplify log_{10}(2)+log_{10}(0.2)

simplify

lo g_{10} (2) + lo g_{10} (0.2)

lo g_{10} (\frac{2}{5})

Decimal Notation

- 0.39794 \dots

Solution steps

lo g_{10} (2) + lo g_{10} (0.2)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (2) + lo g_{10} (0.2) = lo g_{10} (2 \cdot 0.2)

= lo g_{10} (2 \cdot 0.2)

Multiply the numbers:

2 \cdot 0.2 = 0.4

= lo g_{10} (0.4)

0.4 = \frac{4}{10}

= lo g_{10} (\frac{4}{10})

Cancel

\frac{4}{10} : \frac{2}{5}

= lo g_{10} (\frac{2}{5})

2 ln (\frac{2 x + 3}{x ^{2} - 3 x + 2})

ln (\frac{x ^{9} x ^{2} + 5}{( x + 5 ) ^{6}})

ln (\frac{0.01}{( 1 - 0.01 )})

ln (2 x^{4})

ln (\frac{e ^{4}}{t})

What is log_{10}(2)+log_{10}(0.2) ?
The solution to log_{10}(2)+log_{10}(0.2) is log_{10}(2/5)