What is log_{10}(27)+log_{10}(1/9) ?

The solution to log_{10}(27)+log_{10}(1/9) is log_{10}(3)

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simplify log_{10}(27)+log_{10}(1/9)

simplify

lo g_{10} (27) + lo g_{10} (\frac{1}{9})

lo g_{10} (3)

Decimal Notation

0.47712 \dots

Solution steps

lo g_{10} (27) + lo g_{10} (\frac{1}{9})

Apply log rule:

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

lo g_{10} (27) + lo g_{10} (\frac{1}{9}) = lo g_{10} (27 \cdot \frac{1}{9})

= lo g_{10} (27 \cdot \frac{1}{9})

27 \cdot \frac{1}{9} = 3

= lo g_{10} (3)

ln (\frac{5}{9 x ^{9} y})

lo g_{3} (7) - lo g_{3} (8)

2 lo g_{5} (3) + 3 lo g_{5} (2) - \frac{1}{2} lo g_{5} (36)

ln (\frac{6 x}{y})

\frac{3}{4} \cdot lo g_{2} (\frac{3}{4}) + \frac{1}{4} \cdot lo g_{2} (\frac{1}{4})

What is log_{10}(27)+log_{10}(1/9) ?
The solution to log_{10}(27)+log_{10}(1/9) is log_{10}(3)