What is log_{10}(15)+log_{10}(2)-log_{10}(5) ?

The solution to log_{10}(15)+log_{10}(2)-log_{10}(5) is log_{10}(6)

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simplify log_{10}(15)+log_{10}(2)-log_{10}(5)

simplify

lo g_{10} (15) + lo g_{10} (2) - lo g_{10} (5)

lo g_{10} (6)

Decimal Notation

0.77815 \dots

Solution steps

lo g_{10} (15) + lo g_{10} (2) - lo g_{10} (5)

Apply log rule:

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

lo g_{10} (15) + lo g_{10} (2) = lo g_{10} (15 \cdot 2)

= lo g_{10} (15 \cdot 2) - lo g_{10} (5)

Apply log rule:

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

lo g_{10} (15 \cdot 2) - lo g_{10} (5) = lo g_{10} (\frac{15 \cdot 2}{5})

= lo g_{10} (\frac{15 \cdot 2}{5})

Cancel

\frac{15 \cdot 2}{5} : 6

= lo g_{10} (6)

lo g_{7} (49 x)

lo g_{4} (2) + 2 lo g_{4} (7)

lo g_{2} (16 x)

lo g_{4} (x^{2}) + lo g_{4} (x)

lo g_{2} (\frac{8 x ^{2}}{y}) + lo g_{2} (2 x y)

What is log_{10}(15)+log_{10}(2)-log_{10}(5) ?
The solution to log_{10}(15)+log_{10}(2)-log_{10}(5) is log_{10}(6)