What is log_{3}(7)+log_{3}(12)-log_{3}(4) ?

The solution to log_{3}(7)+log_{3}(12)-log_{3}(4) is log_{3}(21)

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simplify log_{3}(7)+log_{3}(12)-log_{3}(4)

simplify

lo g_{3} (7) + lo g_{3} (12) - lo g_{3} (4)

lo g_{3} (21)

Decimal Notation

2.77124 \dots

Solution steps

lo g_{3} (7) + lo g_{3} (12) - lo g_{3} (4)

Apply log rule:

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

lo g_{3} (7) + lo g_{3} (12) = lo g_{3} (7 \cdot 12)

= lo g_{3} (7 \cdot 12) - lo g_{3} (4)

Apply log rule:

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

lo g_{3} (7 \cdot 12) - lo g_{3} (4) = lo g_{3} (\frac{7 \cdot 12}{4})

= lo g_{3} (\frac{7 \cdot 12}{4})

Cancel

\frac{7 \cdot 12}{4} : 21

= lo g_{3} (21)

ln (\frac{e ^{9}}{10})

(lo g_{b} (x) - lo g_{b} (y)) + 4 lo g_{b} (v)

lo g_{4} (\frac{16}{x + 5})

ln (\frac{535.6}{348.1})

lo g_{7} ((a + b) \cdot c)

What is log_{3}(7)+log_{3}(12)-log_{3}(4) ?
The solution to log_{3}(7)+log_{3}(12)-log_{3}(4) is log_{3}(21)