What is log_{12}((12sqrt(13))/(11n)) ?

The solution to log_{12}((12sqrt(13))/(11n)) is 1+log_{12}(sqrt(13))-log_{12}(11)-log_{12}(n)

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simplify log_{12}((12sqrt(13))/(11n))

simplify

lo g_{12} (\frac{12 13}{11 n})

1 + lo g_{12} (13) - lo g_{12} (11) - lo g_{12} (n)

Solution steps

lo g_{12} (\frac{12 13}{11 n})

Apply log rule:

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

lo g_{12} (\frac{12 13}{11 n}) = lo g_{12} (1213) - lo g_{12} (11 n)

= lo g_{12} (1213) - lo g_{12} (11 n)

lo g_{12} (1213) = 1 + lo g_{12} (13)

lo g_{12} (11 n) = lo g_{12} (11) + lo g_{12} (n)

= 1 + lo g_{12} (13) - (lo g_{12} (11) + lo g_{12} (n))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{12} (11) + lo g_{12} (n)) = - lo g_{12} (11) - lo g_{12} (n)

= 1 + lo g_{12} (13) - lo g_{12} (11) - lo g_{12} (n)

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What is log_{12}((12sqrt(13))/(11n)) ?
The solution to log_{12}((12sqrt(13))/(11n)) is 1+log_{12}(sqrt(13))-log_{12}(11)-log_{12}(n)