What is log_{1/3}(21)+log_{3}(14)-log_{3}(18) ?

The solution to log_{1/3}(21)+log_{3}(14)-log_{3}(18) is -log_{3}(21)+log_{3}(7/9)

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simplify log_{1/3}(21)+log_{3}(14)-log_{3}(18)

simplify

lo g_{\frac{1}{3}} (21) + lo g_{3} (14) - lo g_{3} (18)

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

Decimal Notation

- 3

Solution steps

lo g_{\frac{1}{3}} (21) + lo g_{3} (14) - lo g_{3} (18)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{3} (14) - lo g_{3} (18) = lo g_{3} (\frac{14}{18})

= lo g_{\frac{1}{3}} (21) + lo g_{3} (\frac{14}{18})

Cancel the common factor:

2

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

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

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

ln (\frac{0.000408}{0.000231})

ln (2 e^{5 x})

\frac{d}{d x} (ln (4 x - 3)) + ln (2 x)

ln (2.4 \cdot 1 0^{- 12})

lo g_{10} (24) - lo g_{10} (6)

What is log_{1/3}(21)+log_{3}(14)-log_{3}(18) ?
The solution to log_{1/3}(21)+log_{3}(14)-log_{3}(18) is -log_{3}(21)+log_{3}(7/9)