What is log_{10}(6)+log_{10}(5)-log_{10}(15) ?

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

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simplify log_{10}(6)+log_{10}(5)-log_{10}(15)

simplify

lo g_{10} (6) + lo g_{10} (5) - lo g_{10} (15)

lo g_{10} (2)

Decimal Notation

0.30102 \dots

Solution steps

lo g_{10} (6) + lo g_{10} (5) - lo g_{10} (15)

Apply log rule:

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

lo g_{10} (6) + lo g_{10} (5) = lo g_{10} (6 \cdot 5)

= lo g_{10} (6 \cdot 5) - lo g_{10} (15)

Apply log rule:

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

lo g_{10} (6 \cdot 5) - lo g_{10} (15) = lo g_{10} (\frac{6 \cdot 5}{15})

= lo g_{10} (\frac{6 \cdot 5}{15})

Cancel

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

= lo g_{10} (2)

lo g_{10} (\frac{a ^{2}}{b ^{- 3} c ^{4}})

\frac{1}{3} lo g_{b} (x) + 4 lo g_{b} (y) - 3 lo g_{b} (x)

lo g_{10} (x^{4}) y

lo g_{2} (6) + lo g_{2} (3)

lo g_{3} (\frac{c}{27})

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