What is log_{10}(9)+log_{10}(20)-log_{10}(5) ?

The solution to log_{10}(9)+log_{10}(20)-log_{10}(5) is 2log_{10}(6)

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simplify log_{10}(9)+log_{10}(20)-log_{10}(5)

simplify

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

2 lo g_{10} (6)

Decimal Notation

1.55630 \dots

Solution steps

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

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} (5)

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} (5) = lo g_{10} (\frac{9 \cdot 20}{5})

= lo g_{10} (\frac{9 \cdot 20}{5})

Cancel

\frac{9 \cdot 20}{5} : 36

= lo g_{10} (36)

Factor the number:

36 = 6^{2}

= lo g_{10} (6^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (6^{2}) = 2 lo g_{10} (6)

= 2 lo g_{10} (6)

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

ln (5 x^{4})

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

lo g_{b} (\frac{1}{a})

What is log_{10}(9)+log_{10}(20)-log_{10}(5) ?
The solution to log_{10}(9)+log_{10}(20)-log_{10}(5) is 2log_{10}(6)