What is log_{10}(9)+log_{10}(20)-log_{10}(4) ?

The solution to log_{10}(9)+log_{10}(20)-log_{10}(4) is log_{10}(45)

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simplify log_{10}(9)+log_{10}(20)-log_{10}(4)

simplify

lo g_{10} (9) + lo g_{10} (20) - lo g_{10} (4)

lo g_{10} (45)

Decimal Notation

1.65321 \dots

Solution steps

lo g_{10} (9) + lo g_{10} (20) - lo g_{10} (4)

Apply log rule:

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

lo g_{10} (9) + lo g_{10} (20) = lo g_{10} (9 \cdot 20)

= lo g_{10} (9 \cdot 20) - lo g_{10} (4)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (9 \cdot 20) - lo g_{10} (4) = lo g_{10} (\frac{9 \cdot 20}{4})

= lo g_{10} (\frac{9 \cdot 20}{4})

Cancel

\frac{9 \cdot 20}{4} : 45

= lo g_{10} (45)

lo g_{10} (9) + lo g_{10} (20) - lo g_{10} (5)

lo g_{2} (9^{5})

ln (5 x^{4})

- lo g_{10} (6.5 \cdot 1 0^{- 4})

What is log_{10}(9)+log_{10}(20)-log_{10}(4) ?
The solution to log_{10}(9)+log_{10}(20)-log_{10}(4) is log_{10}(45)