What is log_{21}(7)+log_{21}(9)-log_{21}(1/3) ?

The solution to log_{21}(7)+log_{21}(9)-log_{21}(1/3) is log_{21}(189)

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simplify log_{21}(7)+log_{21}(9)-log_{21}(1/3)

simplify

lo g_{21} (7) + lo g_{21} (9) - lo g_{21} (\frac{1}{3})

lo g_{21} (189)

Decimal Notation

1.72169 \dots

Solution steps

lo g_{21} (7) + lo g_{21} (9) - lo g_{21} (\frac{1}{3})

Apply log rule:

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

lo g_{21} (7) + lo g_{21} (9) = lo g_{21} (7 \cdot 9)

= lo g_{21} (7 \cdot 9) - lo g_{21} (\frac{1}{3})

Apply log rule:

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

lo g_{21} (7 \cdot 9) - lo g_{21} (\frac{1}{3}) = lo g_{21} (\frac{7 \cdot 9}{\frac{1}{3}})

= lo g_{21} (\frac{7 \cdot 9}{\frac{1}{3}})

\frac{7 \cdot 9}{\frac{1}{3}} = 189

= lo g_{21} (189)

ln ∣ x - y ∣ - ln (u)

lo g_{10} (x) - 3 lo g_{10} (3) - \frac{1}{2} lo g_{10} (y)

50 ln (\frac{8}{3})

2 ln (9) - 5 ln (3) + ln (4)

lo g_{5} (x^{3} y^{2})

What is log_{21}(7)+log_{21}(9)-log_{21}(1/3) ?
The solution to log_{21}(7)+log_{21}(9)-log_{21}(1/3) is log_{21}(189)