What is log_{5}(w/(2b)) ?

The solution to log_{5}(w/(2b)) is log_{5}(w)-log_{5}(2)-log_{5}(b)

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simplify log_{5}(w/(2b))

simplify

lo g_{5} (\frac{w}{2 b})

lo g_{5} (w) - lo g_{5} (2) - lo g_{5} (b)

Solution steps

lo g_{5} (\frac{w}{2 b})

Apply log rule:

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

lo g_{5} (\frac{w}{2 b}) = lo g_{5} (w) - lo g_{5} (2 b)

= lo g_{5} (w) - lo g_{5} (2 b)

Simplify

lo g_{5} (2 b) : lo g_{5} (2) + lo g_{5} (b)

= lo g_{5} (w) - (lo g_{5} (2) + lo g_{5} (b))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{5} (2) + lo g_{5} (b)) = - lo g_{5} (2) - lo g_{5} (b)

= lo g_{5} (w) - lo g_{5} (2) - lo g_{5} (b)

- (\frac{2}{5} lo g_{2} (\frac{2}{5}) + \frac{3}{5} lo g_{2} (\frac{3}{5}))

ln (\frac{9}{25})

ln (x) + \frac{1}{2} ln (y) + ln (\frac{1}{2}) z

4 lo g_{10} (x) - lo g_{10} (x^{2}) y + 2 lo g_{10} (z)

lo g_{10} (5) - lo g_{10} (y) - lo g_{10} (9 c)

What is log_{5}(w/(2b)) ?
The solution to log_{5}(w/(2b)) is log_{5}(w)-log_{5}(2)-log_{5}(b)