What is log_{5}((5sqrt(11))/(13s)) ?

The solution to log_{5}((5sqrt(11))/(13s)) is 1+log_{5}(sqrt(11))-log_{5}(13)-log_{5}(s)

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simplify log_{5}((5sqrt(11))/(13s))

simplify

lo g_{5} (\frac{5 11}{13 s})

1 + lo g_{5} (11) - lo g_{5} (13) - lo g_{5} (s)

Solution steps

lo g_{5} (\frac{5 11}{13 s})

Apply log rule:

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

lo g_{5} (\frac{5 11}{13 s}) = lo g_{5} (511) - lo g_{5} (13 s)

= lo g_{5} (511) - lo g_{5} (13 s)

lo g_{5} (511) = 1 + lo g_{5} (11)

lo g_{5} (13 s) = lo g_{5} (13) + lo g_{5} (s)

= 1 + lo g_{5} (11) - (lo g_{5} (13) + lo g_{5} (s))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{5} (13) + lo g_{5} (s)) = - lo g_{5} (13) - lo g_{5} (s)

= 1 + lo g_{5} (11) - lo g_{5} (13) - lo g_{5} (s)

ln (x - 2) - ln (x - 1)

ln (\frac{1 + t ^{2} - 2 t}{1 + t ^{2} + 2 t})

ln (\frac{100}{150})

lo g_{2} (x) - lo g_{2} (x^{8})

- (\frac{1}{3} lo g_{e} (\frac{1}{3}) + \frac{2}{3} lo g_{e} (\frac{2}{3}))

What is log_{5}((5sqrt(11))/(13s)) ?
The solution to log_{5}((5sqrt(11))/(13s)) is 1+log_{5}(sqrt(11))-log_{5}(13)-log_{5}(s)