What is log_{9}(27)+log_{9}(sqrt(3)) ?

The solution to log_{9}(27)+log_{9}(sqrt(3)) is 7/4

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simplify log_{9}(27)+log_{9}(sqrt(3))

simplify

lo g_{9} (27) + lo g_{9} (3)

\frac{7}{4}

Decimal Notation

1.75

Solution steps

lo g_{9} (27) + lo g_{9} (3)

Apply log rule:

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

lo g_{9} (27) + lo g_{9} (3) = lo g_{9} (273)

= lo g_{9} (273)

Factor the number:

9 = 3^{2}

= lo g_{3^{2}} (273)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{3^{2}} (273) = \frac{1}{2} lo g_{3} (273)

= \frac{1}{2} lo g_{3} (273)

273 = 3^{\frac{7}{2}}

= \frac{1}{2} lo g_{3} (3^{\frac{7}{2}})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{3} (3^{\frac{7}{2}}) = \frac{7}{2}

= \frac{1}{2} \cdot \frac{7}{2}

\frac{1}{2} \cdot \frac{7}{2} = \frac{7}{4}

= \frac{7}{4}

lo g_{18} (\frac{13 r}{s})

6 ln (x) + 5 ln (y) - 2 ln (z)

lo g_{8} (x) + 3 lo g_{8} (2 x - 5) - 7 lo g_{8} (x - 3)

ln (\frac{e ^{x} ln ( 3 )}{3})

- lo g_{10} (7.5 \cdot 1 0^{- 3})

What is log_{9}(27)+log_{9}(sqrt(3)) ?
The solution to log_{9}(27)+log_{9}(sqrt(3)) is 7/4