What is log_{w}((5x)/(6z)) ?

The solution to log_{w}((5x)/(6z)) is log_{w}(5)+log_{w}(x)-log_{w}(6)-log_{w}(z)

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simplify log_{w}((5x)/(6z))

simplify

lo g_{w} (\frac{5 x}{6 z})

lo g_{w} (5) + lo g_{w} (x) - lo g_{w} (6) - lo g_{w} (z)

Solution steps

lo g_{w} (\frac{5 x}{6 z})

Apply log rule:

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

lo g_{w} (\frac{5 x}{6 z}) = lo g_{w} (5 x) - lo g_{w} (6 z)

= lo g_{w} (5 x) - lo g_{w} (6 z)

lo g_{w} (5 x) = lo g_{w} (5) + lo g_{w} (x)

lo g_{w} (6 z) = lo g_{w} (6) + lo g_{w} (z)

= lo g_{w} (5) + lo g_{w} (x) - (lo g_{w} (6) + lo g_{w} (z))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{w} (6) + lo g_{w} (z)) = - lo g_{w} (6) - lo g_{w} (z)

= lo g_{w} (5) + lo g_{w} (x) - lo g_{w} (6) - lo g_{w} (z)

lo g_{10} (\frac{8 m}{n})

lo g_{9} (k^{2} - 81) - lo g_{9} (k) - 9

2 lo g_{10} (u) - 3 lo g_{10} (v) - 2 lo g_{10} (z)

lo g_{2} (7) + lo g_{2} (3)

ln (\frac{( x y ) ^{2}}{z ^{3}})

What is log_{w}((5x)/(6z)) ?
The solution to log_{w}((5x)/(6z)) is log_{w}(5)+log_{w}(x)-log_{w}(6)-log_{w}(z)