What is log_{16}((9sqrt(r))/s) ?

The solution to log_{16}((9sqrt(r))/s) is 2log_{16}(3)+log_{16}(sqrt(r))-log_{16}(s)

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simplify log_{16}((9sqrt(r))/s)

simplify

lo g_{16} (\frac{9 r}{s})

2 lo g_{16} (3) + lo g_{16} (r) - lo g_{16} (s)

Solution steps

lo g_{16} (\frac{9 r}{s})

Apply log rule:

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

lo g_{16} (\frac{9 r}{s}) = lo g_{16} (9 r) - lo g_{16} (s)

= lo g_{16} (9 r) - lo g_{16} (s)

Simplify

lo g_{16} (9 r) : 2 lo g_{16} (3) + lo g_{16} (r)

= 2 lo g_{16} (3) + lo g_{16} (r) - lo g_{16} (s)

lo g_{10} (a - b) - lo g_{10} (3)

ln (x^{e} e^{x})

ln ∣ x ∣ - 2 ln ∣ x + 1 ∣ + ln ∣ x - 2 ∣ + C

lo g_{3} (\frac{81}{y})

2 ln (3) - 2 ln (2)

What is log_{16}((9sqrt(r))/s) ?
The solution to log_{16}((9sqrt(r))/s) is 2log_{16}(3)+log_{16}(sqrt(r))-log_{16}(s)