What is log_{3}((x+33x)/((x-1)(x-5))) ?

The solution to log_{3}((x+33x)/((x-1)(x-5))) is log_{3}(34x)-log_{3}(x-1)-log_{3}(x-5)

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simplify log_{3}((x+33x)/((x-1)(x-5)))

simplify

lo g_{3} (\frac{x + 33 x}{( x - 1 ) ( x - 5 )})

lo g_{3} (34 x) - lo g_{3} (x - 1) - lo g_{3} (x - 5)

Solution steps

lo g_{3} (\frac{x + 33 x}{( x - 1 ) ( x - 5 )})

Apply log rule:

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

lo g_{3} (\frac{x + 33 x}{( x - 1 ) ( x - 5 )}) = lo g_{3} (x + 33 x) - lo g_{3} ((x - 1) (x - 5))

= lo g_{3} (x + 33 x) - lo g_{3} ((x - 1) (x - 5))

Apply log rule:

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

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

= lo g_{3} (x + 33 x) - (lo g_{3} (x - 1) + lo g_{3} (x - 5))

Add similar elements:

x + 33 x = 34 x

= lo g_{3} (34 x) - (lo g_{3} (x - 1) + lo g_{3} (x - 5))

- (lo g_{3} (x - 1) + lo g_{3} (x - 5)) : - lo g_{3} (x - 1) - lo g_{3} (x - 5)

= lo g_{3} (34 x) - lo g_{3} (x - 1) - lo g_{3} (x - 5)

lo g_{2} (\frac{1}{2} x^{2} y)

ln (\frac{e ^{3} 2}{e ^{\frac{1}{3}}}) - e^{2 l n (2)}

- ln (a) - ln (b)

ln (11 x)

\frac{1}{2} lo g_{a} (x) + 3 lo g_{a} (y) - 4 lo g_{a} (x)

What is log_{3}((x+33x)/((x-1)(x-5))) ?
The solution to log_{3}((x+33x)/((x-1)(x-5))) is log_{3}(34x)-log_{3}(x-1)-log_{3}(x-5)