What is log_{9}(25/36)+log_{3}(54/5) ?

The solution to log_{9}(25/36)+log_{3}(54/5) is 2

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simplify log_{9}(25/36)+log_{3}(54/5)

simplify

lo g_{9} (\frac{25}{36}) + lo g_{3} (\frac{54}{5})

2

Solution steps

lo g_{9} (\frac{25}{36}) + lo g_{3} (\frac{54}{5})

lo g_{9} (\frac{25}{36}) = lo g_{3} (5) - 1 - lo g_{3} (2)

lo g_{3} (\frac{54}{5}) = 3 + lo g_{3} (2) - lo g_{3} (5)

= (lo g_{3} (5) - 1 - lo g_{3} (2)) + (3 + lo g_{3} (2) - lo g_{3} (5))

(lo g_{3} (5) - 1 - lo g_{3} (2)) + (3 + lo g_{3} (2) - lo g_{3} (5)) = lo g_{3} (5) - 1 - lo g_{3} (2) + 3 + lo g_{3} (2) - lo g_{3} (5)

= lo g_{3} (5) - 1 - lo g_{3} (2) + 3 + lo g_{3} (2) - lo g_{3} (5)

Add similar elements:

lo g_{3} (5) - lo g_{3} (5) = 0

= - 1 - lo g_{3} (2) + 3 + lo g_{3} (2)

Add similar elements:

- lo g_{3} (2) + lo g_{3} (2) = 0

= - 1 + 3

Add the numbers:

- 1 + 3 = 2

= 2

ln (4 x)

\frac{1}{2} (ln (3) - ln 2 e^{3 x} + 1)

lo g_{6} (x y^{3} z^{- 2})

lo g_{3} (\frac{27}{x + 7})

ln (l + x^{2} + y^{2}) - ln (x)

What is log_{9}(25/36)+log_{3}(54/5) ?
The solution to log_{9}(25/36)+log_{3}(54/5) is 2