What is log_{5}((xy)/(zt)) ?

The solution to log_{5}((xy)/(zt)) is log_{5}(x)+log_{5}(y)-log_{5}(z)-log_{5}(t)

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simplify log_{5}((xy)/(zt))

simplify

lo g_{5} (\frac{x y}{z t})

lo g_{5} (x) + lo g_{5} (y) - lo g_{5} (z) - lo g_{5} (t)

Solution steps

lo g_{5} (\frac{x y}{z t})

Apply log rule:

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

lo g_{5} (\frac{x y}{z t}) = lo g_{5} (x y) - lo g_{5} (z t)

= lo g_{5} (x y) - lo g_{5} (z t)

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

lo g_{5} (z t) = lo g_{5} (z) + lo g_{5} (t)

= lo g_{5} (x) + lo g_{5} (y) - (lo g_{5} (z) + lo g_{5} (t))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{5} (z) + lo g_{5} (t)) = - lo g_{5} (z) - lo g_{5} (t)

= lo g_{5} (x) + lo g_{5} (y) - lo g_{5} (z) - lo g_{5} (t)

\frac{1}{2} ln (9) - 3 ln (6) + 3 ln (2)

\frac{ln ( 13 ) - 3 ln ( 6 )}{5 ln ( 6 )}

6 lo g_{b} (x + 4) - 7 lo g_{b} (x + 3) + lo g_{b} (x)

lo g_{10} (\frac{x}{4 y})

ln (\frac{1}{1 + 7})

What is log_{5}((xy)/(zt)) ?
The solution to log_{5}((xy)/(zt)) is log_{5}(x)+log_{5}(y)-log_{5}(z)-log_{5}(t)