What is expand log_{3}((4x)/5) ?

The solution to expand log_{3}((4x)/5) is 2log_{3}(2)+log_{3}(x)-log_{3}(5)

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expand log_{3}((4x)/5)

expand

lo g_{3} (\frac{4 x}{5})

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

Solution steps

lo g_{3} (\frac{4 x}{5})

Apply log rule:

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

lo g_{3} (\frac{4 x}{5}) = lo g_{3} (4 x) - lo g_{3} (5)

= lo g_{3} (4 x) - lo g_{3} (5)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{3} (4 x) = lo g_{3} (4) + lo g_{3} (x)

= lo g_{3} (4) + lo g_{3} (x) - lo g_{3} (5)

lo g_{3} (4) = 2 lo g_{3} (2)

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

ln (\frac{x - 1}{x})

- lo g_{10} (1.5 \cdot 1 0^{- 11})

ln (2.2) + (ln (4.3)) + ln (6.15)

ln (\frac{x ^{2} - 6 x - 27}{x - 7})

ln (\frac{( 2 - y )}{( 1 - y )})

What is expand log_{3}((4x)/5) ?
The solution to expand log_{3}((4x)/5) is 2log_{3}(2)+log_{3}(x)-log_{3}(5)