What is log_{3}(8)+log_{3}(c)-log_{3}(4) ?

The solution to log_{3}(8)+log_{3}(c)-log_{3}(4) is log_{3}(2c)

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simplify log_{3}(8)+log_{3}(c)-log_{3}(4)

simplify

lo g_{3} (8) + lo g_{3} (c) - lo g_{3} (4)

lo g_{3} (2 c)

Solution steps

lo g_{3} (8) + lo g_{3} (c) - lo g_{3} (4)

Apply log rule:

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

lo g_{3} (8) + lo g_{3} (c) = lo g_{3} (8 c)

= lo g_{3} (8 c) - lo g_{3} (4)

Apply log rule:

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

lo g_{3} (8 c) - lo g_{3} (4) = lo g_{3} (\frac{8 c}{4})

= lo g_{3} (\frac{8 c}{4})

Simplify

\frac{8 c}{4} : 2 c

= lo g_{3} (2 c)

5 ln (2) - \frac{1}{2} + 5 ln (3) - 5 ln (1) + 1 - 5 ln (2)

lo g_{10} (3 x y^{2})

- lo g_{10} (3.8 \cdot 1 0^{- 6})

ln (\frac{7 + e ^{x}}{7 - e ^{x}})

\frac{1}{2} ln (\frac{1}{4})

What is log_{3}(8)+log_{3}(c)-log_{3}(4) ?
The solution to log_{3}(8)+log_{3}(c)-log_{3}(4) is log_{3}(2c)